The univariate Borel—Tanner distribution has been used extensively in the analysis of data pertaining to biological word frequency, queueing and other branching areas. Tables of the distribution has been given by Owen. With the hope that a bivariate distribution would prove to be as useful as a univariate distribution, a three parameter bivariate Borel—Tanner distribution and its approximation by the bivariate negative binomial distribution is considered.