The dependences of the power loss per cycle on frequency have been investigated in the ranges of 100 Hz≤ f ≤25000 Hz and 0.1 T ≤ B_m ≤ 1.0 T for three main original magnetic states in five sorts of Fe-based nanocrystalline soft magnetic alloys. The measured and calculated results showed that the total power loss per cycle clearly exhibited a nonlinear behavior in the range below 3 kHz-5 kHz depending on both the magnetic state and the value of B_m, whereas it showed a quasi-linear behavior above this range. The total loss was decomposed into hysteresis loss, classical eddy current loss and excess loss, the obvious nonlinear behavior has been confirmed to be completely determined by the dependence of the excess loss on frequency. It has been indicated that the change rate of the excess loss per cycle with respect to frequency sharp decreases with increasing frequency in the range below about 3 kHz-5 kHz, wherease the rate of change slowly varies above this range, thus leading to the quasilinear behavior of the total loss per cycle. In this paper, some linear expressions of the total loss per cycle has been given in a wider medium-frequency segment, which can be used for roughly estimating the total loss. The dependences of the power loss per cycle on frequency have been investigated in the ranges of 100 Hz ≤ f ≤ 25000 Hz and 0.1 T ≤ B_m ≤ 1.0 T for three main original magnetic states in five sorts of Fe-based nanocrystalline soft magnetic alloys. The measured and calculated results showed that the total power loss per cycle clearly exhibited a nonlinear behavior in the range below 3 kHz-5 kHz depending on both the magnetic state and the value of B_m, yet it showed a quasi-linear behavior above this range . The total loss was decomposed into hysteresis loss, classical eddy current loss and excess loss, the obvious nonlinear behavior has been confirmed to be completely determined by the dependence of the excess loss on frequency. It has been indicated that the change rate of the excess loss per cycle with respect to frequency sharp decreases with increasing frequency in the range below about 3 kHz-5 kHz, wherease the rate of change slowly varies above this range, thus leading to the quasilinear behavior of the total loss per cycle. In this paper, some linear expressions of the total loss per cycle has been given in a wider medium-frequency segment, which can be used for roughly estimating the total loss.