  We investigate unitarity within the Complex-Mass Scheme, a convenient
universal scheme for perturbative calculations involving unstable particles in
Quantum Field Theory which guarantees exact gauge invariance. Since this scheme
requires to introduce complex masses and complex couplings, the Cutkosky
cutting rules, which express perturbative unitarity in theories of stable
particles, are no longer valid. We derive corresponding rules for scalar
theories with unstable particles based on Veltman's Largest-Time Equation and
prove unitarity in this framework.
