  We propose a novel method for calculating resonances in three-body Coulombic
systems. The method is based on the solution of the set of Faddeev and
Lippmann-Schwinger integral equations, which are designed for solving the
three-body Coulomb problem. The resonances of the three-body system are defined
as the complex-energy solutions of the homogeneous Faddeev integral equations.
We show how the kernels of the integral equations should be continued
analytically in order that we get resonances. As a numerical illustration a toy
model for the three-$\alpha$ system is solved.
