A theoretical analysis of the differentially coherent phase-shift keying system acting under a wide range of noise and signal conditions is given. In addition to the elemental error rate, it is desirable to know the error rates for sequences of errors, since there is intersymbol dependency in this system. To determine the probability of a sequence ofrerrors requires, at most, integrations over volumes up to2r + 2dimensions, which are performed by Monte Carlo techniques. The analysis and computational schemes are such that any noise and signal statistics, as well as the use of nonlinear devices (noise suppression equipment), can be taken into account in calculating the error rates (for ak-phase system) as long as the resulting joint distributions of the instantaneous SNR at the phase detector can be determined in some form. A sequence ofrerrors requires knowledge of the (r + 1)st-order distribution. Since nothing is known of the joint densities of atmospheric or other non-Gaussian interference, and since many systems have slow enough bit rates for the noise to be independent from one integration period to the next, examples are given for the independent case for Gaussian noise and characteristic samples of atmospheric noise. Results for both constant and slow, flat, Rayleigh fading signal for the two and four phase systems are given, and comparisons of experimental results with the theoretical error rates are made. Also, for comparison, expressions are derived and results given for the error rates corresponding to the above for the coherent PSK system.