Magnetic-field-line merging occurs at a tangential discontinuity in a plasma if regions of finite conductivity occur which are elongated along the direction of current flow. If however they are elongated in a direction perpendicular to the current flow, field-line slippage occurs. In field-line slippage, magnetic field-aligned electric fields occur which allow the frozen-field regions on each side of the finite-conductivity region to undergo different flows. These flows are in a direction so as to decrease magnetic energy and transform it to plasma energy. This is believed to be occurring in auroral arcs. It is suggested herein that since finite conductivity occurs when the local plasma cannot carry the required sheet current, the shape, size and orientation of regions of finite conductivity are determined by local plasma and field properties. Hence, if elongated, these regions may be at an arbitrary angle to the current-flow direction, although still within the plane of the tangential discontinuity. Under these conditions, and also in what is likely to be the commonest situation, that is patches of finite conductivity which are not greatly elongated in any direction, merging and slippage should occur simultaneously.