A method for controlling the transmit power for uplink transmissions on component carriers of a mobile communication system in a power-limited situation, wherein the component carriers have a priority order, the method comprising the following steps performed by a mobile terminal: receiving uplink resource assignments scheduling the uplink transmissions on the component carriers within a transmission time interval, determining for each of a respective one of the uplink transmissions, a transmit power required for transmitting the respective uplink transmission according to its corresponding uplink resource assignment, determining the mobile terminal to be in the power-limited situation when the sum of the determined required transmit powers for transmitting the respective uplink transmissions exceeds the maximum transmit power available to the mobile terminal for uplink transmissions, minus the transmit power required for control signaling on the physical uplink control channel within the same transmission time interval, in case of determining the power-limited situation, reducing the determined transmit power for each of a respective one of the uplink transmissions according to the priority of the component carriers given by the priority order such that the sum of the reduced transmit powers for transmitting the uplink transmissions becomes smaller than or equal to the maximum transmit power available to the mobile terminal for uplink transmissions minus the transmit power required for control signaling on the physical uplink control channel within the same transmission time interval, wherein the step of reducing the determined transmit power does not reduce the transmit power for transmitting the control signaling on the physical uplink control channel, transmitting the uplink transmissions on the component carriers within the transmission time interval, using the reduced transmit power, and wherein each uplink resource assignment is allocating radio resources on one of the component carriers, wherein the processing order of the uplink resource assignments is determined according to the priorities of the component carriers on which the radio resources are allocated by the uplink resource assignments. receiving uplink resource assignments scheduling the uplink transmissions on the component carriers within a transmission time interval, determining for each of a respective one of the uplink transmissions, a transmit power required for transmitting the respective uplink transmission according to its corresponding uplink resource assignment, determining the mobile terminal to be in the power-limited situation when the sum of the determined required transmit powers for transmitting the respective uplink transmissions exceeds the maximum transmit power available to the mobile terminal for uplink transmissions, minus the transmit power required for control signaling on the physical uplink control channel within the same transmission time interval, in case of determining the power-limited situation, reducing the determined transmit power for each of a respective one of the uplink transmissions according to the priority of the component carriers given by the priority order such that the sum of the reduced transmit powers for transmitting the uplink transmissions becomes smaller than or equal to the maximum transmit power available to the mobile terminal for uplink transmissions minus the transmit power required for control signaling on the physical uplink control channel within the same transmission time interval, wherein the step of reducing the determined transmit power does not reduce the transmit power for transmitting the control signaling on the physical uplink control channel, transmitting the uplink transmissions on the component carriers within the transmission time interval, using the reduced transmit power, and wherein each uplink resource assignment is allocating radio resources on one of the component carriers, wherein the processing order of the uplink resource assignments is determined according to the priorities of the component carriers on which the radio resources are allocated by the uplink resource assignments.