The first amplitude analysis of data on ppBAR --> pi-pi+ from the PS17
2 experiment at CERN's LEAR facility is performed to discover the reso
nant content of the NNBAR --> pipi channel in the range 0.36 less-than
-or-equal-to P(lab) less-than-or-equal-to 1.55 GeV/c. Simultaneously f
itting existing data on ppBAR --> pi0pi0, we find just two solutions h
aving acceptable threshold behaviour and continuity in energy. Resonan
t structures in these solutions are studied using self-consistency to
fix the arbitrary overall phase of the amplitudes. Both solutions exhi
bit a rich spectrum of resonances with spins from 0 to 4. This include
s at least one state, with J(PC) = 0++, whose coupling to NNBAR is muc
h larger than would be expected for a simple qqBAR state.