‎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.