The symmetry of solutions and the symmetry of the first integrals of the restricted three-body problem in Nechvile coordinates is examined. The equivalence between the symmetry of solutions and the symmetry of the first integrals is shown. The existence of two families of selfsymmetric solutions, each of which is a function of three arbitrary parameters is proven. An analogous study is performed for the rectilinear three-body problem.
Sternberg Astronomical Institute - Moscow University, Moscow, Russia, 119992, Universitetskij pr., 13