An investigation is performed to determine the response of yielding two-story frames subjected to a white noise ground acceleration. Column stiffnesses of the structural model exhibit a bilinear hysteretic behavior. Empirical data for general yielding systems is obtained by a numerical integration procedure which measures mean square displacement and velocity values at each floor level of the structural model. Results are compatible with known data for linear and nonlinear single degree of freedom systems. Attempts at analytical solutions are limited to two-story frames in which only the first floor yields. The first theoretical solution attempts to predict the behavior of a nonlinear system by modifying stiffness and damping characteristics and studying the resulting system as a linear model. It is found that interstory mean square response is underpredicted with this procedure. The second analytic approach defines an equivalent linear system by matching its response parameters with those obtained from numerical results and calculating frequencies and mode shapes of that equivalent system. Results from this interpretive approach indicate that for systems for which the second slope of the bilinear stiffness relation is a small percentage of the initial slope, a linear system which exhibits the same mean square response levels as the original yielding system does not exist.