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An important alternative distribution to the Weibull, generalized exponen- tial and gamma distributions that is used in survival analysis is the Nadarajah- Haghighi exponential distribution. Similar to the Weibull, generalized exponen- tial and gamma distributions, the Nadarajah-Haghighi exponential distribution is an extension of the well known exponential distribution. In this paper, a copula function commonly used to model very weak linear dependence was used to intro- duced a bivariate Nadarajah-Haghighi distribution. The joint survival function, joint probability density function and joint cumulative distribution were given in closed form. Bayesian method of estimation was used to estimate the model parameters considering the presence of right censoring and covariates. Posterior summaries of interest were obtained via standard Markov Monte Carlo (MCMC ) technique. Two real data sets were used to illustrate the importance and flexi- bility of the bivariate model in comparison with some competing models. It was observed that, the bivariate Nadarajah-Haghighi distribution provides a better flt than bivariate exponential, bivariate Weibull, bivariate generalized exponential and bivariate modified Weibull distributions.