A methodology for calculating analytically various probabilities and statistical properties of run lengths of annual hydrological data has been developed and applied to the first-order Markov processes. In deriving the analytical expressions, the sequential property of the Markovian variables, which reduce the multivariate integral equation into multiplication of various bivariate integrals, has been extensively used. Tables have been provided for the mean variance coefficient of skewness and coefficient of variation of positive run lengths at various truncation levels and first-order serial correlation coefficient. It has been observed that run length properties of the Markov processes are the functions of truncation level and first-order serial correlation coefficient only. As the serial correlation coefficient increases, the positive run length also increases.