The invention relates to a method for connecting a mobile communications connection in a mobile communications network, particularly in a cellular mobile communications network, in the case of temporarily limited accessibility or availability of the mobile communications network due to an overload, between a prioritized first mobile communications terminal device and a non-prioritized second mobile communications terminal device, wherein the non-prioritized mobile communications terminal device is at least partially and at least temporarily blocked due to the overload situation, wherein the first prioritized mobile communications terminal device transmits a call connection attempt, the mobile communications network recognizes the call connection attempt as a prioritized call connection attempt and prioritizes said attempt over other, non-prioritized mobile communications terminal devices and transmits said attempt to the second non-prioritized mobile communications terminal device, wherein the blockage of the second mobile communications terminal device is at least temporarily lifted such that the incoming call may be accepted by the second mobile communications terminal device and the mobile communications connection may be made, the blockage of the second mobile communications terminal device being particularly lifted on the network side or the second mobile communications terminal device particularly having means for recognizing that the call connection attempt is originating from a prioritized mobile communications terminal device and at least temporarily ignoring the blockage thereof.