Recently, it has been observed that a new method for generating the continuous distributions, T-X family, can be quite effectively used to analyze the data in one dimension. The aim of this study was to generalize this method to the two dimensional space so that the marginals would have the T-X distributions. In doing so, several examples and properties of this family have been presented. As an application, a special distribution of this family, called bivariate Weibull-Rayleigh-Rayleigh, was fitted to one data set and showed a better indexes fit.