Classical blind channel equalization methods may not be suitable for systems with nonlinear modulation (e.g., continous phase-modulated signals) because the input to the channel may not be i.i.d. due to the modulator's memory. Moreover, the nonlinear characteristics of the modulator further complicate the channel estimation task. In this correspondence, we derive blind maximum likelihood channel estimation algorithms for nonlinearly modulated signals using a hidden Markov model (HMM) formulation. The proposed method implements a stochastic maximum likelihood approach and is well suited for short data records appearing in TDMA systems. Cramer-Rao bounds are derived, and some illustrative simulations are presented.