Abstract: A reduced state sequence detection algorithm with decision feedback for continuous phase modulation is given and extended to noncoherent detection. This algorithm can greatly reduce the number of states with Viterbi detection. Analysis and simulation results show that the algorithm efficiently reduces the computation complexity with a very small degradation in error performance compared with its optimum maximum likelihood sequence detection, and although noncoherent detection is degraded by 2dB at 10-3 bit error rate compared with coherent detection, it is more appropriate and robust to the situation when the carrier recovery is difficult.