<p>A new kinetic master equation for the generalized Langevin dynamics of a mechanical system undergoing radiative interaction with a broadband electromagnetic field in a squeezed state has been derived from a quantum stochastic differential equation constructed using the algebra of generators of two-quantum stochastic processes. The latter express the Hamiltonian of the radiative interaction in terms of the Ito increments of these processes. The motion of a harmonic oscillator and a free particle has been analyzed using the equation for the Wigner quasiprobability, which is next in the harmonic approximation of the original equation for an open system. Features of the system dynamics in a broadband squeezed field and a broadband field in a classical state have been revealed.</p>