Using time dependent MHD simulations, we study the nature of three-dimensional magnetic reconnection in thin quasi-separatrix layers (QSLs), in the absence of null points. This process is believed to take place in the solar atmosphere, in many solar flares and possibly in coronal heating. We consider magnetic field configurations which have previously been weakly stressed by asymmetric line-tied twisting motions and whose potential fields already possessed thin QSLs. When the line-tied driving is suppressed, magnetic reconnection is solely due to the self-pinching and dissipation of narrow current layers previously formed along the QSLs. A generic property of this reconnection process is the continuous slippage of magnetic field lines along each other, while they pass through the current layers. This is contrary to standard null point reconnection, in which field lines clearly reconnect by pair and abruptly exchange their connectivities. For sufficiently thin QSLs and high resistivities, the field line footpoints slip-run at super-Alfvénic speeds along the intersection of the QSLs with the line-tied boundary, even though the plasma velocity and resistivity are there fixed to zero. The slip-running velocities of a given footpoint have a well-defined maximum when the field line crosses the thinnest regions of the QSLs. QSLs can then physically behave as true separatrices on MHD time scales, since magnetic field lines can change their connections on time scales far shorter than the travel-time of Alfvén waves along them. Since particles accelerated in the diffusive regions travel along the field much faster than the Alfvén speed, slip-running reconnection may also naturally account for the fast motion of hard X-ray sources along chromospheric ribbons, as observed during solar flares.
