The Ericsson power cycles working with ideal Bose and Fermi monoatomic gases are examined. They are conveniently called the Bose and Fermi cycles. Efficiencies of Bose and Fermi cycles are derived (eta(B) and eta(F) respectively). Variations of them with the temperature ratio (tau) and pressure ratio of the cycle are examined. A comparison of the efficiencies with each other and that of the classical Ericsson cycle (eta(Cl)) is made. In the degenerate gas state it is seen that eta(B) < eta(F) < eta(Cl), although eta(B) = eta(F) = eta(Cl) in the classical gas state. In a Bose cycle, it is shown that there is an optimum value for the lowest temperature (T-L) at which the efficiency reaches its maximum value for a given pressure ratio. Furthermore, Bose-Einstein condensation restricts the value of T-L Of a Bose cycle for a given value of P-H. In a Fermi cycle, there is no an optimum value for T-L. However, eta(F) goes to a finite value of less than unity when tau goes to zero.