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Recently, a method for combined noncoherent detection and decoding of trellis-codes (noncoherent coded modulation) has been proposed, which can practically approach the performance of coherent detection. Here, we successfully apply the technique to the detection of Continuous Phase Modulation (CPM), coded or uncoded. Both full and partial response CPM schemes with arbitrary modulation index are considered. This method is based on multiple-symbol observations, such that the observations are time-overlapped. The results show that most CPM schemes require short observations to achieve almost the same power efficiency as optimally detected coherent CPM. Compared to the previously proposed methods for noncoherent detection that can approach the coherent performance, the required observation length is much shorter and also the decoding complexity is much lower. A new trellis diagram for noncoherent CPM is suggested for simplifying the analysis and the decoder structure. The error performance for uncoded CPM is evaluated by using the union bound technique applied on the symbol-difference trellis diagram. For the coded case a pair-state trellis is required. Very efficient sub-optimal decoding algorithms with very small degradation may implement the noncoherent decoder. The performance achieved with these algorithms is demonstrated by simulations.