A multi-mode electro-mechanical variable speed transmission capable of providing two power split operation modes and at least one fixed output-to-input speed ratio operation mode. The transmission includes an input shaft, an output system, at least one planetary gear set having at least a first, second and third co-axial rotatable components, two electric machines, and at least one torque transfer device. The first co-axial rotatable component couples to the first electric machine with a constant speed ratio; the second co-axial rotatable component couples to the output system with a constant speed ratio; and the third co-axial rotatable component couples to the input shaft with a constant speed ratio; the second electric machine selectively couples to two different co-axial rotatable components of the planetary gear set with two different speed ratios. The transmission is configured to unload the torque transfer device, adjust engine power, shift one of the electric machines to a freewheeling state, and actively synchronize the speed of the electric machines with the speed of one of the engagement positions of the torque transfer device.