A generalized Hylleraas-type basis set with three nonlinear parameters is p
roposed to study three-body systems interacting via coulomb forces within t
he framework of non-relativistic quantum mechanics. This basis set improves
the rate of convergence with respect to previous ones, specially for nonsy
mmetric systems and excited states of two electron atoms: Accurate binding
energies and other properties for S-states of helium-like ions, muonic mole
cules and the positronium negative ion are reported.