To examine the effect of quantum degeneracy on the cycle efficiency, Stirling power cycles working with ideal Bose and Fermi gases are thermodynamically analysed. These cycles are called Bose and Fermi cycles. Efficiency expressions of Bose and Fermi cycles are derived (eta (B) and eta (F) respectively). Variations of them with the temperature ratio (tau = T-L/T-H) and specific volume ratio (r(v) = v(H)/v(L)) are examined. Efficiencies are compared with each other and that of the classical Stirling cycle (eta (C)) It is shown that eta (F) and eta (B) depend on both temperatures and specific volumes of the cycle although eta (C) depends on only the temperatures of the cycle. It is also seen that eta (F) < eta (B) < eta (C). The quantities Delta eta (F) = eta (C) - eta (F) and Delta eta (B) = eta (C) - eta (B) go to zero at the classical gas conditions. Under degeneracy gas conditions, however, Delta eta (B) is greater than zero and it has one maximum and one minimum value while TL decreases. On the other hand, Delta eta (F) has no extremum point and increases continuously with decreasing T-L. eta (F) and eta (B) decrease with increasing r(v) when v(H) is constant although they increase when v(L) is constant. Under the conditions that the working gas remains a completely degenerate Bose gas throughout the cycle, it is seen that eta (B) goes to 0.4 instead of unity when tau goes to zero.