A hybrid vehicle control device, characterized by comprising: an engine; a motor provided to a drive system from the engine to a drive wheel (RL, RR), and having a drive motor function as well as an engine startup motor function; a first clutch for switching to a hybrid vehicle travel mode by engaging and an electric automobile travel mode by disengaging, the first clutch being installed between the engine and the motor; an automatic transmission for automatically varying a gear ratio, the automatic transmission being installed between the motor and the drive wheel (RL, RR); characterized by further comprising a second clutch for maintaining a slip-engaged state during engine startup control, the second clutch being installed in any position from the motor to the drive wheel (RL, RR); first simultaneous process control means that, during simultaneous processing of startup control of the engine initiated based on a startup request, and downshift control of the automatic transmission initiated based on a shift request while driving, maintains the slip-engaged state of the second clutch until synchronization of the first clutch is completed to execute startup control of the engine first, and then executes the downshift control once the startup control is completed. second simultaneous process control means that, during simultaneous processing of startup control of the engine initiated based on a startup request, and downshift control of the automatic transmission initiated based on a shift request while driving, executes startup control of the engine and the downshift control in parallel, and prior to completion of startup of the engine by synchronization of the first clutch, completes downshifting by bringing about application of an engaged element of the automatic transmission to be applied for downshifting while the slip-engaged state of the second clutch is maintained, bringing the state of the automatic transmission to a state of transmission of drive power of the shift position subsequent to the downshift; and simultaneous process selection control means that, before simultaneously processing startup control of the engine and the downshift control, in a case where the torque outputtable by the motor subsequent to downshifting is less than a predetermined torque for the purpose of starting up the engine, selects the first simultaneous process control, or in a case where the torque outputtable by the motor subsequent to downshifting is equal to or greater than the predetermined torque for the purpose of starting up the engine, selects the second simultaneous process control, whereupon simultaneous processing of the startup control of the engine and the downshift control is executed by the selected simultaneous process control means. an engine; a motor provided to a drive system from the engine to a drive wheel (RL, RR), and having a drive motor function as well as an engine startup motor function; a first clutch for switching to a hybrid vehicle travel mode by engaging and an electric automobile travel mode by disengaging, the first clutch being installed between the engine and the motor; an automatic transmission for automatically varying a gear ratio, the automatic transmission being installed between the motor and the drive wheel (RL, RR); characterized by further comprising a second clutch for maintaining a slip-engaged state during engine startup control, the second clutch being installed in any position from the motor to the drive wheel (RL, RR); first simultaneous process control means that, during simultaneous processing of startup control of the engine initiated based on a startup request, and downshift control of the automatic transmission initiated based on a shift request while driving, maintains the slip-engaged state of the second clutch until synchronization of the first clutch is completed to execute startup control of the engine first, and then executes the downshift control once the startup control is completed. second simultaneous process control means that, during simultaneous processing of startup control of the engine initiated based on a startup request, and downshift control of the automatic transmission initiated based on a shift request while driving, executes startup control of the engine and the downshift control in parallel, and prior to completion of startup of the engine by synchronization of the first clutch, completes downshifting by bringing about application of an engaged element of the automatic transmission to be applied for downshifting while the slip-engaged state of the second clutch is maintained, bringing the state of the automatic transmission to a state of transmission of drive power of the shift position subsequent to the downshift; and simultaneous process selection control means that, before simultaneously processing startup control of the engine and the downshift control, in a case where the torque outputtable by the motor subsequent to downshifting is less than a predetermined torque for the purpose of starting up the engine, selects the first simultaneous process control, or in a case where the torque outputtable by the motor subsequent to downshifting is equal to or greater than the predetermined torque for the purpose of starting up the engine, selects the second simultaneous process control, whereupon simultaneous processing of the startup control of the engine and the downshift control is executed by the selected simultaneous process control means.