A general expression is derived for the average infinitesimal-impulse-response matrix of a conservative classical system in a canonical ensemble. The equations of motion are taken as ẋn=Xn, where the X's, as well as the energy E, are functions of the x's but not of their time derivatives. The Liouville equation Σ∂ẋn∂xn=0 is assumed, but it is not required that the equations of motion be derivable from a Hamiltonian. If they are, the x's are the canonical coordinates and momenta. The result found is gmn(τ)=Φmn(τ)kT, (τ>=0), where ∊gmn(τ) is the average increment in xm at time t resulting from an infinitesimal increment ∊ externally induced in xn at time t-τ, Φmn(τ) is the covariance <xm(t)(∂E∂xn)'>, where the prime denotes argument t-τ, k and T are Boltzmann's constant and absolute temperature. This relation is derived as a direct consequence of the fact that two initially isolated systems in equilibrium at identical temperatures remain in equilibrium when weakly coupled to each other.