This paper is a sequel to a previous paper which considered the error performance of binary DPSK transmission for the case of noise and general cochannel interferences. The present work extends that analysis to include multiphase signaling. Whereas the binary analysis produced exact expressions for the probability of error, the extension toM-ary DPSK considered here leads to upper and lower bounds to the symbol error probability. The bounds have a ratio of 2. However, by a heuristic argument it is possible to estimate the proximity of the error probability to one of the bounds, and so the uncertainty in the approximation is small enough to make the results quite usable for systems design. Computations are displayed for quaternary (M = 4) single difference (conventional) DPSK.