We develop space-time trellis coded (STC) schemes using continuous-phase modulation (CPM). We employ the Rimoldi model of CPM to create a decomposed model of STC-CPM. The decomposition separates the coding from the modulation. The space-time encoding and the inherent CPM encoding is combined into a single trellis encoder on the ring of integers modulo-p. This is followed by a bank of memoryless modulators. The model allows the search for good space-time codes to take into account the inherent encoding of the modulation.