Minimum shift keying (MSK) is a power/bandwidth efficient continuous phase modulation technique with constant envelope and, hence, is attractive for use in wireless systems employing inexpensive nonlinear power amplifiers. Space-time coding provide high transmission rates, diversity and coding gains. In this paper, by combining these two techniques, full-rate full-diversity space-time trellis codes for MSK employing two and three transmit antennas are proposed for quasi-static Rayleigh fading channels. Their frame error rate performances are evaluated by computer simulations when one and four receive antennas are used and it is shown that the proposed codes have good error performance. (c) 2005 Elsevier Ltd. All rights reserved.