This paper concerns situations in which a p x p covariance matrix is a function of an unknown q x 1 parameter vector y-sub-c. Notation is defined in the second section and some algebraic results used in subsequent sections are given. Section 3 deals with asymptotic properties of generalized least squares (G.L.S.) estimators of y-sub-o. Section 4 concerns methods for obtaining estimates of parameters in certain linear covariance structures. (Author/KM) (38pp.)