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The morphological types of galaxies in nine clusters in the redshift range 0.1 lesssim z lesssim 0.25 are derived from very good seeing images taken at the NOT and the La Silla-Danish telescopes, with all galaxies at MV < -20 and within the central ~1 Mpc2 area being classified. With the purpose of investigating the evolution of the fraction of different morphological types with redshift, we compare our results with the morphological content of nine distant clusters studied by the MORPHS group, five clusters observed with HST/WFPC2 at redshift z = 0.2-0.3, and Dressler's large sample of nearby clusters. After having checked the reliability of our morphological classification both in an absolute sense and relative to the MORPHS scheme, we analyze the relative occurrence of elliptical, S0, and spiral galaxies as a function of the cluster properties and redshift. We find a large intrinsic scatter in the S0/E ratio, mostly related to the cluster morphology. In particular, in our cluster sample, clusters with a high concentration of ellipticals display a low S0/E ratio and, vice versa, low concentration clusters have a high S0/E. At the same time, the trend of the morphological fractions (%E's, %S0's, %Sp's) and of the S0/E and S0/Sp ratios with redshift clearly points to a morphological evolution: as the redshift decreases, the S0 population tends to grow at the expense of the spiral population, whereas the frequency of E's remains almost constant. We also analyze the morphology-density (MD) relation in our clusters and find that—similarly to higher redshift clusters—a good MD relation exists in the high-concentration clusters, while it is absent in the less concentrated clusters. Finally, the comparison of the MD relation in our clusters with that of the MORPHS sample suggests that the transformation of spirals into S0 galaxies becomes more efficient with decreasing local density.