This paper deals with the attitude control of an underactuated spacecraft that has fewer than three actuators. Even though such spacecrafts are known as uncontrollable, restricted missions are possible with controlling two-axis attitude angles. A variable speed control moment gyroscope is considered as an actuator. It is a kind of momentum exchange device and it shows highly nonlinear dynamical properties. Speed commands are generated by kinematic equations represented by Euler angles. A control law, that is designed to make a spacecraft follow the speed commands, is derived by the backstepping method. Angular speeds are estimated from the attitude measurements. Several estimation methods have been compared.