We consider the system of N (≥ 2) elastically colliding hard balls with masses ℳ1, . . . , ℳN, radius r, moving uniformly in the flat torus double-struck T signvL= ℝv/L · ℤv, v ≥ 2. It is proved here that the relevant Lyapunov exponents of the flow do not vanish for almost every (N + 1)-tuple (ℳ1, . . . , ℳN; L) of the outer geometric parameters.