Methods for the analysis of panel data under a continuous-time Markov model are proposed. We present procedures for obtaining maximum likelihood estimates and associated asymptotic covariance matrices for transition intensity parameters in time homogeneous models, and for other process characteristics such as mean sojourn times and equilibrium distributions. Generalizations to handle covariance analysis and to the fitting of certain nonhomogeneous models are presented, and an example based on a longitudinal study of the smoking habits of school children is discussed. Questions of embeddability and estimation are examined.