A speed changing apparatus for changing an input speed at an input shaft (45, 55) to an output speed at an output shaft (46, 56), the apparatus comprising: a coaxial pair of internal gear engagement members including a large internal gear engagement member (41, 51) having an engagement pitch diameter A and a small internal gear engagement member (44, 54) having an engagement pitch diameter D; a coaxial pair of external gear engagement members including a large external gear engagement member (42, 52) having an engagement pitch diameter B and a small external gear engagement member (43, 53) having an engagement pitch diameter C; the large external gear engagement member (42, 52) engaging with the large internal gear engagement member (41, 51) and the small external gear engagement member (43, 53) engaging with the small internal gear engagement member (44, 54), forming two engaging pairs; and a carrier member (45E, 55E) connected to one of the input and output shafts (45, 46; 55, 56) of the apparatus; wherein two members (42, 43; 51, 54) of one of the two coaxial pairs being fixed together to move epicyclically on the carrier (45E, 55E); and one member (41; 52) of the other of the two coaxial pairs being fixed to a frame of the apparatus and the other member (44; 53) being connected to the other of the input and output shafts (45, 46, 55, 56); the apparatus being characterized in that the four gear engagement members (41, 42, 43, 44; 51, 52, 53, 54) satisfying the dimensional relationship of A = K+i, B = K, C = K-j and D = K+i-j wherein K is pitch diameter of the large external gear engagement member (42, 52), i is the difference between pitch diameters of the large internal gear engagement member (41, 51) and the large external gear engagement member (42, 52) and j is the difference between pitch diameters of the large internal gear engagement member (41, 51) and the small internal gear engagement member (44, 54). a coaxial pair of internal gear engagement members including a large internal gear engagement member (41, 51) having an engagement pitch diameter A and a small internal gear engagement member (44, 54) having an engagement pitch diameter D; a coaxial pair of external gear engagement members including a large external gear engagement member (42, 52) having an engagement pitch diameter B and a small external gear engagement member (43, 53) having an engagement pitch diameter C; the large external gear engagement member (42, 52) engaging with the large internal gear engagement member (41, 51) and the small external gear engagement member (43, 53) engaging with the small internal gear engagement member (44, 54), forming two engaging pairs; and a carrier member (45E, 55E) connected to one of the input and output shafts (45, 46; 55, 56) of the apparatus; wherein two members (42, 43; 51, 54) of one of the two coaxial pairs being fixed together to move epicyclically on the carrier (45E, 55E); and one member (41; 52) of the other of the two coaxial pairs being fixed to a frame of the apparatus and the other member (44; 53) being connected to the other of the input and output shafts (45, 46, 55, 56); the apparatus being characterized in that the four gear engagement members (41, 42, 43, 44; 51, 52, 53, 54) satisfying the dimensional relationship of A = K+i, B = K, C = K-j and D = K+i-j wherein K is pitch diameter of the large external gear engagement member (42, 52), i is the difference between pitch diameters of the large internal gear engagement member (41, 51) and the large external gear engagement member (42, 52) and j is the difference between pitch diameters of the large internal gear engagement member (41, 51) and the small internal gear engagement member (44, 54).