Suppose that a random processZ(s;t), indexed in space and time, has spatio-temporal stationary covarianceC(h;u), whereh∈ ℝd(d≥ 1) is a spatial lag andu∈ ℝ is a temporal lag. Separable spatio-temporal covariances have the property that they can be written as a product of a purely spatial covariance and a purely temporal covariance. Their ease of definition is counterbalanced by the rather limited class of random processes to which they correspond. In this article we derive a new approach that allows one to obtain many classes of nonseparable, spatio-temporal stationary covariance functions and fit several such classes to spatio-temporal data on wind speed over a region in the tropical western Pacific ocean.