This paper investigates the error rate performance of parallel combinatorial spread spectrum (PC/SS) communicaion systems that use coherent and differential multiphase modulation: multiphase parallel combinatorial spread spectrum (MPC/SS) communication systems. The PC/SS systems are multicode SS systems based on orthogonal pseudo-noise (PN) sequences. Data is transmitted by delivering a combination of multiple PN sequences among a set of pre-assigned PN sequences. In the MPC/SS systems, every PN sequence on transmission is modulated by q-ary coherent or differential phase shift keying (PSK). Symbol error rate (SER) and average bit error rate (BER) in coherent and differential MPC/SS systems are investigated. The BER comparison between the MPC/SS systems and simple multicode SS systems with q-ary coherent and differential PSK is also presented. Numerical results show that the MPC/SS systems are superior to the conventional q-ary PSK systems, if they have equal spectral efficiency.