Advanced modulation/demodulation techniques which are robust in the presence of phase and frequency uncertainties continue to be of interest to communication engineers. The authors are particularly interested in techniques which accommodate slow channel phase and frequency variations with minimal performance degradation and which alleviate the need for phase and frequency tracking loops in the receiver. They investigate the performance sensitivity to frequency offsets of a modulation technique known as binary double differential phase shift keying (DDPSK) and compare it to that of classical binary differential phase shift keying (DPSK). They also generalize their analytical results to include n/sup -th/ order, M-ary DPSK. The DDPSK (n=2) technique was first introduced in the Russian literature circa 1972 and was studied more thoroughly in the late 1970s by Pent and Okunev. They present an expression for the symbol error probability that is easy to derive and to evaluate numerically. They also present graphical results that establish when, as a function of the signal energy-to-noise ratio and normalized frequency offset, binary DDPSK is preferable to binary DPSK with respect to performance in additive white Gaussian noise. Finally, they provide insight into the optimum receiver from a detection theory viewpoint.>