TITLE The muonic helium atom as a classical three-body problem AUTHORS T.J.Stuchi$^1$, A.C.B.Antunes$^1$ and M.A.Andreu$^2$. 1) Instituto de F\'{\i}sica, Universidade Federal do Rio de Janeiro, Caixa Postal 68.528, 21945-970 Rio de Janeiro, RJ, Brazil. e--mail: tstuchi@if.ufrj.br 2) Dept. Matem\`atica Aplicada i An\`alisi, Univ. Barcelona, Gran Via 585, 08007--Barcelona (Spain). e--mail: mangel@maia.ub.es ABSTRACT: We study the classical problem of the muonic helium atom, a helium atom with one of its electrons replaced by a muon. Firstly, we establish the connection of the model with the one-dimensional frozen planetary approximation of the helium atom and find that there is classically stable motion for the configuration alpha--electron--muon, and no stable motion for the alpha--muon--electron configuration. After that, we introduce the restricted muonic helium problem, a model for the movement of an electron in the potential of the alpha/muon pair moving in a circular orbit. In this model, the equilibrium points, their associated Lyapunov families of periodic orbits and their stability parameters have been studied. The most interesting feature is the stability of the Halo orbits, for a range of energy values. The vicinity of the alpha particle is also studied examining Poincar\'e sections for increasing energy values showing an increase of the chaotic motion.