We study the nonlinear response of a periodically driven dissipative two-state system. The exact formal solution in the form of a series in the number of system transitions is derived. The series is summed in analytic form in the parameter region where incoherent transitions prevail. We also present the exact solution for the time evolution of the system in the entire region of temperatures and driving strength for a special value of the Ohmic viscosity. The destruction of quantum coherence by incoherent processes which are induced by the fluctuating and the driving forces is discussed on the basis of these solutions.