A power source apparatus for a hydraulic actuator, comprising: a hydraulic pump which drives the hydraulic actuator; a generator-motor capable of operating as an electric generator and an electric motor; an engine to which the hydraulic pump and the generator-motor are connected; an electric storage device which is charged by operation of the generator-motor as an electric generator, and which is capable of supplying charged electric power to the generator-motor in order to cause the generator-motor to operate as an electric motor so as to assist driving of the hydraulic pump; a pump pressure detector which detects a discharge pressure of the hydraulic pump as a load pressure of the hydraulic pump; and a controller which implements horsepower control for determining a flow rate for the hydraulic pump on the basis of first characteristics and second characteristics that each define a maximum input setting for the hydraulic pump by the discharge pressure of the hydraulic pump and the flow rate of the hydraulic pump, and the discharge pressure detected by the pump pressure detector, wherein the first characteristics are set in such a manner that the maximum input setting of the pump is greater than a maximum output of the engine throughout a whole pressure range (Pp1 - Pp3) of the discharge pressure of the hydraulic pump, characterized in that the second characteristics are set in such a manner that the maximum input setting for the hydraulic pump is greater than the maximum output of the engine when the discharge pressure is at a predetermined reference pressure, gradually becomes smaller as the discharge pressure changes from the reference pressure towards higher pressure, and becomes smaller than the maximum output of the engine when the discharge pressure is at maximum pressure being higher than the reference pressure, and, in the horsepower control, the controller is configured to: (i) determine the flow rate on the basis of the first characteristics when the discharge pressure detected by the pump pressure detector is less than a set pressure and when a state where the discharge pressure is equal to or greater than the set pressure has not continued for a set time period; and (ii) determine the flow rate on the basis of the second characteristics when the state where the discharge pressure is equal to or greater than the set pressure has continued for the set time period. a hydraulic pump which drives the hydraulic actuator; a generator-motor capable of operating as an electric generator and an electric motor; an engine to which the hydraulic pump and the generator-motor are connected; an electric storage device which is charged by operation of the generator-motor as an electric generator, and which is capable of supplying charged electric power to the generator-motor in order to cause the generator-motor to operate as an electric motor so as to assist driving of the hydraulic pump; a pump pressure detector which detects a discharge pressure of the hydraulic pump as a load pressure of the hydraulic pump; and a controller which implements horsepower control for determining a flow rate for the hydraulic pump on the basis of first characteristics and second characteristics that each define a maximum input setting for the hydraulic pump by the discharge pressure of the hydraulic pump and the flow rate of the hydraulic pump, and the discharge pressure detected by the pump pressure detector, wherein the first characteristics are set in such a manner that the maximum input setting of the pump is greater than a maximum output of the engine throughout a whole pressure range (Pp1 - Pp3) of the discharge pressure of the hydraulic pump, characterized in that the second characteristics are set in such a manner that the maximum input setting for the hydraulic pump is greater than the maximum output of the engine when the discharge pressure is at a predetermined reference pressure, gradually becomes smaller as the discharge pressure changes from the reference pressure towards higher pressure, and becomes smaller than the maximum output of the engine when the discharge pressure is at maximum pressure being higher than the reference pressure, and, in the horsepower control, the controller is configured to: (i) determine the flow rate on the basis of the first characteristics when the discharge pressure detected by the pump pressure detector is less than a set pressure and when a state where the discharge pressure is equal to or greater than the set pressure has not continued for a set time period; and (ii) determine the flow rate on the basis of the second characteristics when the state where the discharge pressure is equal to or greater than the set pressure has continued for the set time period. (i) determine the flow rate on the basis of the first characteristics when the discharge pressure detected by the pump pressure detector is less than a set pressure and when a state where the discharge pressure is equal to or greater than the set pressure has not continued for a set time period; and (ii) determine the flow rate on the basis of the second characteristics when the state where the discharge pressure is equal to or greater than the set pressure has continued for the set time period.