To express in Spanish that something must have happened, as when making an assumption or wondering what must have happened, we can use the verb deber in two different ways:
We can use deber conjugated in El Pretérito Perfecto (followed by an infinitive). For example:
Manuela ha debido llamar a la policía.Manuela must have called the police.
Todavía no han llegado; su avión ha debido retrasarse.They haven't arrived yet; their flight must have had a delay.
Sara ha debido de dejar a su hijo en la guardería esta mañana.Sara must have left her son at the nursery this morning.
Cristina ha debido de ser una buena profesora; sus estudiantes le han comprado flores.Cristina must have been a good teacher; her students bought her some flowers.
Here we are not talking about obligation, which is one of the uses of the modal verb deber, but instead are wondering/assuming what must have happened. The reason to make such an assumption is very often expressed by a fact.
"Cristina ha debido de ser una buena profesora." (assumption)
"Sus estudiantes le han comprado flores." (fact)
The same thing can be expressed using this structure with deber. Have a look at the examples again:
Manuela debe haber llamado a la policía.Manuela must have called the police.
Todavía no han llegado; su avión debe haberse retrasado.They haven't arrived yet; their flight must have had a delay.
Debe de haber llovido esta noche, porque los coches están mojados.It must have rained tonight because the cars are wet.
As you can see from the previous examples, when we use deber with this nuance of assumption/wondering, we can optionally use the preposition "de" after deber.
When the main verb of the sentence is a pronominal verb (uses a reflexive pronoun) you can place the pronoun either in front of the main verbal structure or attached to haber. For example:
Su avión se ha debido retrasar.His plane must have been delayed.
Su avión ha debido retrasarse.His plane must have been delayed.
Su avión se debe haber retrasado.His plane must have been delayed.
Su avión debe haberse retrasado.His plane must have been delayed.
This would be incorrect:
"Su avión debe haber retrasado se.
"Su avión ha debido se retrasar.
"Su avión ha se debido retrasar.
Note that when we use the modal verb deber conjugated in:
"Ella debió aceptar el dinero."
"Ella debió haber aceptado el dinero."
the meaning is generally different. It would normally be translated as "should have done something" instead.
See also Deber versus Deber de (obligation and assumption) and Deber in El Conditional Simple + haber + participle = should have
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