Am I right to assume that these essentially translate into English as the same thing? Otherwise, could you explain any other differences in meaning that might exist?
1) Su avión ha debido retrasarse
2) Su avión debe haberse retrasado
AND that adding 'de' also makes no difference to the meaning (other than maybe 'strengthening' the assumption as we learned about here: Spanish modal verb Deber versus Deber de (obligation and assumption))?
Yes, both structures convey the same, it's always expressing an assumption of what "must have happened". The use of "de" is optional as you can use it or drop it when we're talking about assumptions.
The only other possible interpretation from "el avíon ha debido retresarse" (not debe haberse retrasado) could be the more literal "the plane has had to be delayed", but, for this I'm pretty sure most people would use "tener que" instead: "ha tenido que retrasarse".
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