An engine start control apparatus for a hybrid electric vehicle, wherein: the hybrid electric vehicle is provided with an engine and a motor; the engine and the motor are connected to each other through a first clutch whose transmitted torque capacity is adjustable; the hybrid electric vehicle starts the engine by applying the first clutch and cranking the engine with a driving effort of the motor; the engine start control apparatus employs a first start mode and a second start mode; the first start mode is a mode in which the engine start control apparatus starts the engine from rest in response to driver's accelerator operation; the second start mode is a mode in which the engine start control apparatus starts the engine from rest in response to a factor other than driver's accelerator operation; and the engine start control apparatus sets smaller the transmitted torque capacity of the first clutch during cranking of the engine when in the second start mode than when in the first start mode; characterized in that the engine start control apparatus starts the engine in the second start mode, in response to a condition that a maximum possible motor torque outputted from the motor decreases below a predetermined value while the engine is at rest; and the engine start control apparatus performs a process while starting the engine in the second start mode in response to the condition, wherein the process includes: setting a driving torque transmitted to a driving wheel during cranking such that the driving torque is equal to a driving torque transmitted to the driving wheel during cranking in the first start mode; and setting the transmitted torque capacity of the first clutch during cranking of the engine such that the transmitted torque capacity of the first clutch during cranking of the engine decrease in accordance with the maximum possible motor torque. the hybrid electric vehicle is provided with an engine and a motor; the engine and the motor are connected to each other through a first clutch whose transmitted torque capacity is adjustable; the hybrid electric vehicle starts the engine by applying the first clutch and cranking the engine with a driving effort of the motor; the engine start control apparatus employs a first start mode and a second start mode; the first start mode is a mode in which the engine start control apparatus starts the engine from rest in response to driver's accelerator operation; the second start mode is a mode in which the engine start control apparatus starts the engine from rest in response to a factor other than driver's accelerator operation; and the engine start control apparatus sets smaller the transmitted torque capacity of the first clutch during cranking of the engine when in the second start mode than when in the first start mode; characterized in that the engine start control apparatus starts the engine in the second start mode, in response to a condition that a maximum possible motor torque outputted from the motor decreases below a predetermined value while the engine is at rest; and the engine start control apparatus performs a process while starting the engine in the second start mode in response to the condition, wherein the process includes: setting a driving torque transmitted to a driving wheel during cranking such that the driving torque is equal to a driving torque transmitted to the driving wheel during cranking in the first start mode; and setting the transmitted torque capacity of the first clutch during cranking of the engine such that the transmitted torque capacity of the first clutch during cranking of the engine decrease in accordance with the maximum possible motor torque. setting a driving torque transmitted to a driving wheel during cranking such that the driving torque is equal to a driving torque transmitted to the driving wheel during cranking in the first start mode; and setting the transmitted torque capacity of the first clutch during cranking of the engine such that the transmitted torque capacity of the first clutch during cranking of the engine decrease in accordance with the maximum possible motor torque.