We investigate the impact of hierarchical galaxy merging on the statistics of gravitational lensing of distant sources. Since no definite theoretical predictions for the merging history of luminous galaxies exist, we adopt a parametrized prescription, which allows us to adjust the expected number of pieces comprising a typical present galaxy at z=0.65. The existence of global parameter relations for elliptical galaxies and constraints on the evolution of the phase space density in dissipationless mergers, allow us to limit the possible evolution of galaxy lens properties under merging. We draw two lessons from implementing this lens evolution into statistical lens calculations: (1) The total optical depth to multiple imaging (e.g. of quasars) is quite insensitive to merging. (2) Merging leads to a smaller mean separation of observed multiple images. Because merging does not reduce drastically the expected lensing frequency it cannot make $��$-dominated cosmologies compatible with the existing lensing observations. A comparison with the data from the HST Snapshot Survey shows that models with little or no evolution of the lens population are statistically favored over strong merging scenarios. The specific merging scenario proposed by Toomre (1977) can be rejected (95\% level) by such a comparison. Some versions of the scenario proposed by Broadhurst, Ellis \& Glazebrook (1992), are statistically acceptable.

uuencoded postscript file with figures