We have measured the branching ratios for {Mathematical expression} annihilation at rest into π+π-η and π+π-η′ in hydrogen gas in two data samples that have different fractions of S-wave and P-wave initial states. The branching ratios are derived from a comparison with the topological branching ratio for {Mathematical expression} annihilations into four charged pions of (49±4)% and the branching ratio into π+π-π+π-π0 of (18.7±1.6)%. We find a significant reduction of the branching ratios from P-states for {Mathematical expression} and π+π-η′ in comparison to S-state annihilation. {Mathematical expression} In a partial wave analysis of the π+π-η Dalitz plot we find the following contributions: Phase space, {Mathematical expression}, ηρ0 and f2(1270)η: {Mathematical expression} We find a 2 σ effect for the reaction {Mathematical expression}, {Mathematical expression}, with a branching ratio of (0.13±0.07)·10-3. For η' production we give a branching ratio of {Mathematical expression} of (1.81±0.44)·10-3 from3S1. We estmate a contribution of about 0.3·10-3 for ρη' from P-states. The ratio of ρη and ρη' rpoduction is used to test the validity of the quark line rule. In the π+π-π+π- γ final state we do not observe the reaction {Mathematical expression}, ω→π+π-λ and derive an upper limit of 3·10-3 for decay mode ω→π+π-λ. © 1990 Springer-Verlag.