A vehicle drive system including a transmission has a gear set with first, second, third and fourth elements. The second element connects with an output shaft of the transmission. The system has a transmission housing and a first electric motor having an output shaft connecting with the first element for driving the first element in response to a first electrical signal. A second electric motor has an output shaft connecting with the fourth element for driving the fourth element in response to a second electrical signal. The motors operate together to cause transmission ratios to change steplessly through an infinite number of ratios between maximum and minimum values.