We have used self-consistent numerical simulations of N-body systems to investigate encounters between spherical non-rotating galaxies. In our simulations, the galaxies were represented by Plummer spheres (ρ∝r–5 with isotropic velocity distribution, and we considered collisions along hyperbolic, as well as a few parabolic, orbits. Pairs of galaxies with several different mass ratios (1:1, 1:2, 1:4 and 1:8) were included. We analysed the effects on the internal structure of the galaxies caused by collisions that did not result in mergers after one Hubble time, quantitatively estimating the changes in linear size, mass and energy, and discussing their possible correlations with the orbital parameters. Besides this, we used the results of collisions that ended up in mergers to investigate the structure of the remnants (with respect to binding energy, mass loss, linear size and flattening). We also obtained the density profiles of the remnants, which are well described by an r–γ law profile with 3<γ<3.7. Finally, from the analysis of collisions that ended up in mergers and of those that did not, we established a range of initial velocities and impact parameters that serves as a merging criterion.