- The 2s2p 1P and 3P autoionizing states of heliumlike ions are studied via an implementation of the Feshbach projection method within the framework of Z-dependent perturbation theory. These same states are also studied by a more straightforward (nonprojected) application of Z-dependent perturbation theory that has features similar to those of the stabilization method. The computational and theoretical advantages of applying the Feshbach method within Z-dependent perturbation theory are emphasized. Results for all two-electron ions with Z=2 to 10 are tabulated and compared with experiment and with other very accurate theoretical results for these systems. Included in these results are estimates of the resonance positions, energy shifts, and widths of these autoionizing states. 1990 The American Physical Society.