Recent syntactic theory has highlighted the importance of peripheral constructions such as the comparative correlative construction. This construction involves a pair of filler-gap constructions with unusual properties. The first is a subordinate clause and the second a main clause. The construction has a number of related constructions. A version of HPSG, which assumes hierarchies of phrase types, can provide satisfactory analyses both for the comparative correlative constructions and for the related constructions. The two clauses in the comparative-correlative construction can be analysed as non-standard head-filler phrases differing from standard headfiller phrases in certain respects. The construction as a whole can be analyzed as a non-standard head-adjunct phrase, in which the head and the phrase have different categories.