A simple time series model for bivariate exponential variables having first-order auto-regressive structure is presented. The linear random coefficient difference equation model is an adaptation of the New Exponential Autoregressive model (NEAR (2)). The process is Markovian in the bivariate sense and has correlation structure analogous to that of the Gaussian AR(1) bivariate time series model. The model exhibits a full range of positive correlations and cross-correlations. With some modification in either the innovation or the random coefficients, the model admits some negative values for the cross- correlations. The marginal processes are shown to have correlation structure of ARMA (2,1) models.