We consider a transmission system, where the emitted symbols are subject to unknown nonlinear intersymbol interference. Several methods have been proposed in the literature to mitigate the degradation introduced by such channels. However, the problem of non- linear channel identification in the presence of carrier phase noise has not been addressed previously. In this paper, we derive an iterative receiver structure to detect the transmitted symbols, jointly with phase and channel estimation. At each iteration, the channel para- meters are refined based on the expectation-maximization (EM) approach. Also, a pseudo maximum-likelihood (pseudo-ML) carrier recovery, operating in a decision-directed mode, re-estimates the time-varying phase at each iteration. The proposed technique is semi-blind, since a short training sequence is needed to initialize the phase and channel coefficients properly. We show that the proposed scheme allows symbol detection performances close to the genie-aided detector with data-aided channel coefficient estimation. Moreover, a theoretical analysis of the residual phase error confirms that coherent detection in the presence of strong phase noise is achieved. Numerical simulations are presented for systems with severe nonlinear distortions, including satellite communications with nonlinear amplifiers and coherent optical fiber transmissions