See below for updated code
I'm trying to use knockout with typescript but it seems I'm not able to bind my typescript viewmodel to my view... it seems I have an issue with the this but I don't understand why... 
The this.UserList is undefined when calling the Fill method
Here is my viewModel:
module ViewModels {
    export class UserViewModel {
        constructor() {
            this.UserList = ko.observableArray<KnockoutObservable<Models.User>>([]);
            this.RemoveItem = <(user: KnockoutObservable<Models.User>) => void> this.RemoveItem.bind(this);
            this.AcceptItem = <(user: Models.User) => void> this.AcceptItem.bind(this);
            this.AddItem = <() => void> this.AddItem.bind(this);
        }
        public UserList: KnockoutObservableArray<KnockoutObservable<Models.User>>;
        public Fill() {
            $.ajax({
                type: "POST",
                url: "/Guest/LoadGuest/",
                success: data=> {
                    $(data).each((index: any, item)=> {
                        var guest = new Models.User();
                        guest.FirstName = ko.observable(item.firstName);
                        guest.LastName = ko.observable(item.lastName);
                        guest.IsNew = ko.observable(false);
                        this.UserList.push(ko.observable(guest));
                    });
                }
            });
        }
        public AddItem() {
            var guest = new Models.User();
            guest.FirstName = ko.observable("");
            guest.LastName = ko.observable("");
            guest.IsNew = ko.observable(true);
            this.UserList.push(ko.observable(guest));
        }
        public AcceptItem(user: Models.User) {
            user.IsNew = ko.observable(false);
        }
        public RemoveItem(user: KnockoutObservable<Models.User>) {
            this.UserList.remove(user);
        }
    }
}
Here is my View:
<table>
    <thead>
        <tr><th>Prénom</th><th>Nom de famille</th></tr>
    </thead>
    <tbody data-bind="foreach: UserList">
        <tr data-bind="if:IsNew">
            <td><input type="text" data-bind="text: FirstName" /></td>
            <td><input type="text" data-bind="text: LastName" /></td>
            <td><a data-bind="click:$parent.AcceptItem">OK</a><a data-bind="click:$parent.RemoveItem">Annuler</a></td>
        </tr>
        <tr data-bind="if:!IsNew">
            <td data-bind="text: FirstName"></td>
            <td data-bind="text: LastName"></td>
            <td></td>
        </tr>
    </tbody>
</table>
<a id="AddGuest" data-bind="click:AddItem">Add</a>
@section scripts{
    <script src="~/Scripts/models/ModelBase.js"></script>
    <script src="~/Scripts/models/User.js"></script>
    <script src="~/Scripts/viewmodels/UserViewModel.js"></script>
    <script>
        var vm = new ViewModels.UserViewModel();
        vm.Fill();
        ko.applyBindings(vm);
    </script>
}
Here is my model:
 module Models{
     export class User extends Models.ModelBase {
         constructor() {
             super();
         }
         public FirstName: KnockoutObservable<string>;
         public LastName: KnockoutObservable<string>;
         public Age: KnockoutObservable<Age>;
     }
     export class Age {
         public ID: KnockoutObservable<number>;
         public Description: KnockoutObservable<string>;
     }
 }
New working code for helping purposed:
ViewModel:
module ViewModels {
    export class UserViewModel {
        constructor() {
        }
        public UserList: KnockoutObservableArray<Models.User> = ko.observableArray<Models.User>([]);
        public Fill = () => {
            $.ajax({
                type: "POST",
                url: "/Guest/LoadGuest/",
                success: data=> {
                    for (var i = 0; i < data.length; i++) {
                        var item = data[i];
                        var guest = new Models.User();
                        guest.FirstName(item.firstName);
                        guest.LastName(item.lastName);
                        guest.Age().Description("Test Age");
                        guest.IsNew(false);
                        this.UserList.push(guest);
                    }
                }
            });
        }
        public AddItem = () => {
            var guest = new Models.User();
            guest.FirstName = ko.observable("");
            guest.LastName = ko.observable("");
            guest.IsNew(true);
            this.UserList.push(guest);
        }
        public AcceptItem = (user: Models.User) => {
            user.IsNew(false);
        }
        public RemoveItem = (user: Models.User)  => {
            this.UserList.remove(user);
        }
    }
}
Model:
 module Models{
    export class ModelBase{
        constructor() {
            this.IsNew = ko.observable(false);
        }
        public IsNew: KnockoutObservable<boolean>;
    }
     export interface IUser {
         FirstName: KnockoutObservable<string>;
         LastName: KnockoutObservable<string>;
         Age: KnockoutObservable<Age>;
     }
     export class User extends Models.ModelBase implements IUser {
         constructor() {
             super();
             this.FirstName = ko.observable("");
             this.LastName = ko.observable("");
             this.Age = ko.observable(new Age());
         }
         public FirstName: KnockoutObservable<string>;
         public LastName: KnockoutObservable<string>;
         public Age: KnockoutObservable<Age>;
     }
     export class Age {
         constructor() {
             this.ID = ko.observable(null);
             this.Description = ko.observable("");
         }
         public ID: KnockoutObservable<number>;
         public Description: KnockoutObservable<string>;
     }
 }
View:
<table>
        <thead>
            <tr><th>Prénom</th><th>Nom de famille</th><th>Age</th></tr>
        </thead>
        <tbody data-bind="foreach: UserList">
            <tr data-bind="ifnot:$data.IsNew">
                <td data-bind="text: FirstName"></td>
                <td data-bind="text: LastName"></td>
                <td data-bind="text: Age().Description"></td>
            </tr>
            <tr data-bind="if:$data.IsNew">
                <td><input type="text" data-bind="value: FirstName" /></td>
                <td><input type="text" data-bind="value: LastName" /></td>
                <td><input type="text" data-bind="value: Age().Description" /></td>
                <td><a data-bind="click:$root.AcceptItem">OK</a><a data-bind="click:$root.RemoveItem">Annuler</a></td>
            </tr>
        </tbody>
</table>
    <a id="AddGuest" data-bind="click:AddItem">Add</a>
@section scripts{
    <script src="~/Scripts/models/ModelBase.js"></script>
    <script src="~/Scripts/models/User.js"></script>
    <script src="~/Scripts/viewmodels/UserViewModel.js"></script>
    <script>
        var vm = new ViewModels.UserViewModel();
        vm.Fill();
        ko.applyBindings(vm);
    </script>
}
                If you want this to be bound to the UserViewModel that then maybe use this approach:
module ViewModels {
    export class UserViewModel {
        UserList: KnockoutObservableArray<KnockoutObservable<Models.User>> = ko.observableArray<KnockoutObservable<Models.User>>([]);
        Fill = () => {
            $.ajax({
                type: "POST",
                url: "/Guest/LoadGuest/",
                success: data => {
                    $(data).each((index: any, item)=> {
                        var guest = new Models.User();
                        guest.FirstName = ko.observable(item.firstName);
                        guest.LastName = ko.observable(item.lastName);
                        guest.IsNew = ko.observable(false);
                        this.UserList.push(ko.observable(guest));
                    });
                }
            });
        }
        AddItem = () => {
            var guest = new Models.User();
            guest.FirstName = ko.observable("");
            guest.LastName = ko.observable("");
            guest.IsNew = ko.observable(true);
            this.UserList.push(ko.observable(guest));
        }
        AcceptItem = (user: Models.User) => {
            user.IsNew = ko.observable(false);
        }
        RemoveItem = (user: KnockoutObservable<Models.User>) => {
            this.UserList.remove(user);
        }
    }
}
Here's a TypeScript Playground to demo
You can read an explanation of the approach being used here: http://blogs.msdn.com/b/typescript/archive/2013/08/06/announcing-0-9-1.aspx (check "Better 'this' handling)
By the way, I suspect where you have KnockoutObservable<Models.User> you should actually have Models.User and when you have this.UserList.push(ko.observable(guest)); you actually should have this.UserList.push(guest);.  I haven't changed the code sample in case I missed something.
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