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Symbol error probability bounds for maximum likelihood sequence detection (MLSD) of continuous phase modulation (CPM) signals are studied. The calculation of the upper bound is based on the transfer function technique, which has been generalized. A new method for constructing a lower bound for CPM systems is proposed. From numerical comparisons, it can be seen that the proposed algorithm can substantially improve the lower bound compared to previous approaches by considering the entire set of transmitted data sequences and not only the worst case. This generalized algorithm may be applied to any system which can be described as finite state machine.