We have studied fragmentation properties of projectiles in peripheral heavy-ion collisions within a statistical ensemble approach. Distributions of projectile fragments are calculated for the reaction systems86 Kr on58,64 Ni and are compared to the experimental data for the same reactions at projectile energy of 15 MeV/nucleon. We assume that the projectile nuclei capture many neutrons from the targets as a result of the multinucleon transfer reactions (direct and fast reactions) at the first step of the dynamical stage of the collisions, and then the excited spectators are formed during the preequilibrium process (multistep reactions) long before the statistical equilibrium stage, and the deexcitation processes for the hot sources are simulated within the statistical multifragmentation model. It is seen that predicted results are in satisfactory agreement with experimental data.