A nonparametric Bayesian multiple comparisons problem (MCP) for dependence parameters in I bivariate exponential populations is studied. A simple method for pairwise comparisons of these parameters is also suggested. The methodology by Gopalan and Berry (1998) is extended using Dirichlet process priors, applied in the form of baseline prior and likelihood combination to provide the comparisons. Computation of the posterior probabilities of all possible hypotheses are carried out through a Markov Chain Monte Carlo, Gibbs sampling, due to the intractability of analytic evaluation. The process of MCP for the dependent parameters of bivariate exponential populations is illustrated with a numerical example.