This paper presents an analytical study of the covariance kernels of a damped linear two-degree-of-freedom system that is subjected to spatially correlated nonstationary stochastic excitation consisting of modulated white noise. A unit-step intensity function and an exponential function, resembling the envelope of a typical earthquake, are considered in conjunction with a propagating disturbance. Results of the analysis are used to determine the dependence of the peak transient mean-square response of the system on the uncoupled frequency ratios, mass ratios, wave propagation speed, shape of the intensity function, and system damping.