The system of falling balls is a hyperbolic system with singularities, which was introduced by Wojtkowski in 1990. The main, long standing conjecture is whether that sytem is ergodic or not. Sinai and Chernov developed, in 1987, a powerful mechanism for hyperbolic systems with singularities that gives ergodicity of such sytems, by checking, if the dynamical system is 'locally' and 'globally' ergodic. We make a first step towards the solution of this challenging task by proving that the system of \(N\) falling balls is globally ergodic.