We study degenerate two-photon micromasers pumped by cascade three-level atoms, where each atomic energy level has a different linewidth. Our model allows us to recover the ordinary two-photon micromaser situation when these widths vanish. In the limit of large linewidths we obtain a two-photon laser model. We show that trapping states are extremely sensitive to atomic decay, even when the decay time is small in comparison to the transit time through the cavity. Unlike the one-photon micromaser, they are sensitive to the linewidth of the upper, as well as the lower energy level. We have also studied the effects of atomic decay on the starting time of micromasers and on the noise. We found that there is a significant difference between the behavior of two-photon micromasers and lasers as we change the ratio of the widths of the upper and lower levels.