In this paper we will discuss some properties of McElroy's measure of goodness of fit for Zellner's seemingly unrelated regression equations (McELRoY (1977)). Amongst them are asymptotic properties. The same will be done for another goodness-of-fit measure, the squared sample correlation coefficient of (11-10I)y and (f/-10I)y- where is the theoretical value of the dependent variable y and MI is the variance of y. A comparison will be made between the two measures and it turns out that McElroy's measure possesses more desirable characteristics in case all equations contain a constant term.