RxJS Observables nested subscriptions?

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

You can find more details in previous answers :

Your example would read as :

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

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