The oscillator representation is applied to calculate the energy spect
rum of three-body Coulomb systems with total angular momentum J. For t
hree-body Coulomb systems with J = 1 and arbitrary masses the region o
f stability is determined. For the systems (A(+)A(-)e(-)), (pe(-)C(+))
, (pB(-)e(-)), and (D(+)e(-)e(+)), the values of the critical masses o
f the particles A, B, C, and D are obtained as m(A) = 2.22m(e), m(B) =
1.49m(e), m(C) = 2.11m(e), and m(D) = 4.15m(e).