International audienceIn [1], a state space model was derived for the demodulation of Continuous Phase Modulation (CPM) signals, based on which the demodulation problem was solved through the symbol-by-symbol Bayesian estimation built around the MAP Symbol-by-symbol Detector (MAPSD). In this paper, a new state space model considered in the augmented state composed of the symbol and the phase state is proposed and the corresponding modified MAPSD demodulation scheme is presented. The main contribution of the paper however consists in deriving optimal and suboptimal symbol-by-symbol MAP detection schemes for MIMO systems operating with CPM signals. For this, a state model description of the corresponding demodulation problem is introduced based on which two CPM-MIMO Bayesian demodulators are proposed. The first one uses a Zero Forcing (ZF) pre-processing block to separate the different CPM signals followed by a bank of MAPSD based CPM demodulators. The second demodulator consists in a joint decision feedback (DF) CPM-MIMO MAPSD detector. Simulations confirm the good performance in term of BER of both proposed structures. Particularly, high BER's performance of the partially joint CPM-MIMO-MAPSD/DF is recorded and an emphasis is made on the implementation simplicity of this new detector with no constraint on the modulation index or the alphabet size