Angular 5 : Property 'then' does not exist on type 'Observable<any>'

You can call then on a Promise object, so because your service returns an Obaservable object, you need to transform into a Promise with the toPromise() method and use catch method to manage error in this way:

getUsers(){
    this.authService.getUsers()
    .toPromise()
    .then((res) => {
      this.user = res;
      console.log(this.user);
    })
    .catch(err=> { console.log(err) });
  }

Here you can see a DEMO. That's all.

"then" is a promise concept, RxJS is a bit different. If you want to sequence multiple calls, then you need to use forkJoin. If you just want to have a success handler, then use subscribe and catch.

getUsers(){
    this.authService.getUsers().subscribe((res) => {
      this.user = res;
      console.log(this.user);
    }).catch((err) => {
      console.log(err);
    });
  }

Make sure you understand the difference between promise and observable (Angular - Promise vs Observable) and make appropriate design decision.