Continuous phase modulation (CPM) is a non-linear power/bandwidth efficient modulation method. Linear modulation methods such as phase shift keying or quadrature amplitude modulation produce large power drain at the power amplifier of the transmitter. Therefore CPM may be an alternative to these modulations in relay/cooperative systems because of its constant envelope property, which enables us to use inexpensive and energy-efficient non-linear power amplifiers. In this study, the authors investigate optimum distributed space-time CPM trellis codes for amplify and forward relaying systems with one to four relays and specifically consider minimum shift keying and quaternary continuous phase frequency shift keying with modulation indices of 1/2 and 1/4. Novel distributed space-time CPM trellis codes are obtained. Error performances of the novel codes and their classical counterparts are compared over frequency non-selective quasi-static Rayleigh-fading channels using the Viterbi algorithm at the destination terminal and superiority of the novel codes are presented.