A complex preposition is a multi-word preposition. The Cambridge Grammar of the English Language (CGEL) says of complex prepositions, In the first place, there is a good deal of inconsistency in the traditional account, as reflected in the practice of dictionaries, as to which combinations are analysed as complex prepositions and which as sequences of adverb + preposition. For example, owing to and out of are listed as prepositions, but according to, because of, and instead of are treated as adverb + preposition. Modern descriptive grammars have tended to extend the category of complex prepositions, and there is accordingly some variation in dictionary practice, depending on how far they are influenced by such work. CGEL generally argues against a complex preposition analysis, and favours a "layered head analysis" for expressions like in front of the car. In this analysis, in front is a PP, which is head of a larger PP that has of the car as a complement.
