RxJS Observables nested subscriptions?

As mentioned in comments, you are looking for the flatMap operator.

You can find more details in previous answers :

• How to do the chain sequence in rxjs
• Why do we need to use flatMap?

Your example would read as :

this.returnsObservable1(...)
  .flatMap(success => this.returnsObservable2(...))
  .flatMap(success => this.returnsObservable3(...))
  .subscribe(success => {(...)});