In most experimental studies of the shock-wave/boundary-layer interaction at a compression corner the boundary layer upstream of the interaction has developed in zero-pressure-gradient conditions. However, in many practical situations the boundary layer upstream of the interaction is subject to adverse or favourable pressure gradients, and hence is in a non-equilibrium state. This paper presents the results of a series of experiments on the interaction at a compression corner where the boundary layer upstream of the corner is disturbed by air injected through a porous surface. The results are thus of direct interest to the design of transpiration-cooled aerodynamic surfaces. However, the boundary-layer profiles upstream of the interaction also have many similarities to those in an adverse pressure gradient, so that the results also give some indication of the effects of an isentropic compression upstream of the interaction. The results are used to discuss existing correlations for upstream influence and to study conditions for incipient separation. The experiments were made at Mach numbers of 1·8, 2·6, 2·7 and 2·9, with corner angles of 8°, 10°, 12°, 13° and 14°.