There are different ways to express continuity in Spanish. One of them is with the verb "quedarse".
It is formed with the verb quedar in its reflexive form followed by the gerund of the main verb.
Quedar(se) [conjugated] + [gerund of main verb]
The nuance here is "to continue doing something" or "to carry on doing something".
This structure can be used in all tenses.
Have a look and listen to these examples:
Miguel siempre se queda mirándome a los ojos cuando estamos juntos.Miguel always looks [continuously looks] into my eyes when we are together.
Nos quedamos esperando el autobús hasta tarde.We kept waiting for the bus until late.
Antes siempre me quedaba trabajando hasta tarde. Ahora no.Before, I used to continue working until late. Not any more.
No me gusta que os quedéis viendo películas hasta tan tarde.I don't like that you stay up watching films so late.
Remember to use the gerund form (English -ing form) after the verb quedarse.
Se quedó mirando al bebé con dulzura.
Se quedó mirar/mira/mirado al bebé con dulzura.
She kept looking at the baby sweetly.
Extra note: It is important to know that in Spanish, this sometimes implies that the action "suddenly starts at that moment and then continues". For example: I am walking and cross paths with a man, then he suddenly looks at me (he wasn't looking at me before) and doesn't look away but carries on looking. In this case I'd say:
Mientras caminaba, un hombre se quedó mirándome.While I was walking, a man started (and continued) looking at me.
For other ways of expressing continuity of an action see also Using verbs seguir/continuar + gerund = to keep on [doing something]
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