This paper presents an HPSG analysis of the Czech periphrastic past and conditional at the morphology-syntax interface. After clarifying the status of Czech auxiliaries as words rather than affixes, we discuss the fact that the past tense exemplifies the phenomenon of zero periphrasis, where a form of the main verb normally combined with an auxiliary can stand on its own in some paradigm cells. We argue that this is the periphrastic equivalent of zero exponence, and show how the phenomenon can be accommodated within a general theory of periphrasis, where periphrasis is a particular instance of a mismatch between morphology and syntax.