Independence, stationarity, homogeneity, trend, and periodicity tests are applied on 48-year-long complete and 79-year-long incomplete maximum daily rainfall series recorded at Alexandria, Egypt, and on 61-year-long maximum daily rainfall series recorded at Antalya, Turkey, which are located at the southeastern and northeastern shores of the Mediterranean Sea. The results indicate no significant trend and no periodicity in mean, and both series are independent and homogeneous. Linear regression trend test applied to the 10 % highest part of the Alexandria series indicated a significant increasing trend. Next, frequency analysis is applied on each of these series by the probability distributions of Gumbel, general extreme-values, three-parameter log-normal, Pearson-3, log-Pearson-3, log-logistic, generalized Pareto, and Wakeby. The distributions, except for the generalized Pareto and Wakeby, pass the chi (2) and Kolmogorov-Smirnov goodness-of-fit tests at 90 % probability. By visual inspection of the plots of histograms together with the probability density functions, and by the results of the chi (2), Kolmogorov-Smirnov, and probability plot correlation coefficient tests, the general extreme-value distribution whose parameters are computed by the method of probability-weighted moments is deemed to be suitable for these two maximum daily rainfall series.