  We describe partial-wave analyses of the systems \pi-\eta and \pi-\eta'
produced in interactions of a \pi- beam (190 GeV/c) with a liquid hydrogen
target. The data were recorded during the 2008 COMPASS run, where a slow
recoiling proton (|t|>0.1 GeV^2) was required by the trigger. We compare
analyses of the \pi-\eta and \pi-\eta' data. Significant contributions can be
attributed to the resonances a_2(1320), observed in the D_+-wave, and
a_4(2040), observed in the G_+-wave. Between the two systems, we find similar
compositions of the even partial waves D_+ and G_+ after taking phase-space
factors into account, but a much enhanced P_+-wave in \pi-\eta'. Relative
phase-differences indicate a large incoherent contribution of in the P_+-wave
of the \eta'\pi- system, but other interpretations are not excluded. The known
resonances a_2(1320), a_4(2040) and their parameters could be extracted from
the data; their branchings are found to roughly agree with predictions from
\eta\eta' mixing.
