The invention discloses a multiple speed transmission. A family of transmissions produces at least eight forward and one reverse speed ratio by selective engagement of various combinations of three clutches or brakes. Each transmission includes two fixed gearing arrangements that establish fixed speed relationships between an input shaft, and output shaft, and four other elements. Specifically, the input shaft is constrained to rotate at a speed between that of the first and second elements while the output shaft is constrained to rotate at a speed between that of the third and fourth elements. Additional gearing, clutches, and brakes establish specified selective speed relationships among these elements.