For estimating the population variance S ² _y of study variable y , a class of chain estimators of S ² _y has been proposed in the presence of two auxiliary variables x and z by using known information on population mean and variance of the second auxiliary variable z . In this proposed class, the second auxiliary variable z is directly highly correlated with the first auxiliary variable x , whereas the variable z is correlated with the variable y due to only the high correlation between the variables y and x . Another generalized class of estimators of S ² _y has also been considered by using the same available information of auxiliary variable z when both the auxiliary variables x and z are directly highly correlated with the study variable y . The asymptotic expressions for the mean square errors and their optimum values have been obtained. A comparison between the two proposed classes of estimators of S ² _y has been made empirically.