Quasi-separatrix layers are regions in space where the mapping of field line connectivity changes especially rapidly. These layers have been suggested as special locations in three-dimensional magnetic fields that may host magnetic reconnection. Previous investigations have been analytical and have taken different simplifying assumptions to investigate the problem. This paper takes a numerical approach to investigate the dynamical properties of quasi-separatrix layers. The magnetic topology is stressed using drivers suggested by the analytical investigations but modified to fit the adopted boundary conditions. The experiments show that current does accumulate at specific locations in the numerical domain. The current magnitude and location depend strongly on the profile of the imposed driver, and they are found to be generated by the changes in field line parts imposed by the driving. They are therefore the manifestation of free magnetic energy in the perturbed magnetic field. After the stressing of the field has stopped, it is found that the plasma pressure is able to balance the Lorentz force of the stressed magnetic field and prevent a continued growth of the current amplitude in the current layers. Field-line changes are produced in the experiments that include magnetic resistivity. The reconnection takes place at locations where the electric field component along the magnetic field is large. The changes in field-line connectivity initiate flow velocities across the magnetic field lines at only a small fraction of the local Alfv¿n velocity. ¿ 2000 American Geophysical Union