This paper derives a multinomial logit form for dynamic discrete choice models of optimal stopping and suggests a two-step estimator. The first stage estimates nonparametrically the choice probability of terminal state next period. The second stage is an implementation of modified multinomial logit estimation. This paper also suggests semiparametric conditional choice probability (CCP) estimators for discrete choice dynamic models allowing for unobserved individual heterogeneity. I describe a modified Expectation-Maximization (EM) algorithm that involves nonparametric first stage estimation.