We have investigated the doubly excited 1,3Pe and 1,3Do non-autoionizing states of two-electron highly stripped atoms within the framework of the Ritz variational principle. Highly correlated wave functions are used to represent the correlation effect between the charge particles. Precise non-relativistic energy eigenvalues of 2pnp 1Pe(n = 3–7), 2pnp 3Pe
(n = 2–6) and 2pnd 1,3Do
(n = 3–7) states for the systems N5+, O6+, F7+, Ne8+, Na9+ and Mg10+ are reported. The present results for 2pnp 1,3Pe state energies of O6+ and 2pnd 1,3Do state energies of N5+ are accurate in precision compared with the available theoretical results. The wavelengths for 2pnp 1Pe → 2pn′ d
1Do (n, n′ ⩽ 6) and 2pnp 3Pe → 2pn′d 3Do (n, n′ ⩽ 6) transitions and the effective quantum numbers (n*) for 2pnp 1,3Pe and 2pnd 1,3Do states have been calculated.