We consider the estimation of credit rating transitions based on continuous-time observations. Through simple examples and using a large data set from Standard and Poor's, we illustrate the difference between estimators based on discrete-time cohort methods and estimators based on continuous observations. We apply semi-parametric regression techniques to test for two types of non-Markov effects in rating transitions: Duration dependence and dependence on previous rating. We find significant non-Markov effects, especially for the downgrade movements.