A relatively complete discussion is provided for the limiting distributions of certain sample correlation coefficients and sample correlation ratios. It is assumed for the random variablesXandYthat the conditional distribution ofY, givenX=x, is multivariate normal with a constant, but unknown, covariance matrix and that the distribution ofXhas finite fourth moments. The sample coefficients are then based on a random sample from the (X, Y)-distribution. For the case of a univariate random variableXthe limit laws are shown to depend on theX-distribution only through its coefficient of excess. In other cases they are determined from the coefficients of excess of univariate distributions closely related to the distribution ofX.