Context. Understanding the formation, evolution and present-day properties of the cosmic web and objects forming it is an important task in cosmology. Aims: We compare the galaxy populations in superclusters of different morphology in the nearby Universe (180 h-1 Mpc ≤ d ≤ 270 h-1 Mpc) to see whether the inner structure and overall morphology of superclusters are important in shaping galaxy properties in superclusters. Methods: We find supercluster morphology with Minkowski functionals and analyse the probability density distributions of colours, morphological types, stellar masses, star formation rate (SFR) of galaxies, and the peculiar velocities of the main galaxies in groups in superclusters of filament and spider types, and in the field. We test the statistical significance of the results with the KS test. Results: The fraction of red, early-type, low SFR galaxies in filament-type superclusters is higher than in spider-type superclusters; in low-density global environments their fraction is lower than in superclusters. In all environments the fraction of red, high stellar mass, and low SFR galaxies in rich groups is higher than in poor groups. In superclusters of spider morphology red, high SFR galaxies have higher stellar masses than in filament-type superclusters. Groups of equal richness host galaxies with larger stellar masses, a larger fraction of early-type and red galaxies, and a higher fraction of low SFR galaxies, if they are located in superclusters of filament morphology. The peculiar velocities of the main galaxies in groups from superclusters of filament morphology are higher than in those of spider morphology. Groups with higher peculiar velocities of their main galaxies in filament-type superclusters are located in higher density environment than those with low peculiar velocities. There are significant differences between galaxy populations of the individual richest superclusters. Conclusions: Both local (group) and global (supercluster) environments and even supercluster morphology play an important role in the formation and evolution of galaxies. Differences in the inner structure of superclusters of filament and spider morphology and the dynamical state of galaxy groups in them may lead to the differences found in our study. Appendices are available in electronic form at http://www.aanda.org