Summary: We estimate the reliability of parallel systems with two components. We assume that strengths of these components follow a bivariate exponential (BVE) distribution. These two components are subjected to a common stress which is independent of the strength of the components. If the strengths \((X_1,X_2)\) are subjected to a common random stress \((Y)\), then the reliability of a system or system reliability \((R)\) is given by \(R=P[Y< \text{Max} (X_1,X_2)]\). We estimate \(R\) when \((X_1,X_2)\) have different BVE models proposed by A. Marshall and I. Olkin [J. Ann. Stat. Assoc. 62, 30-44 (1967; Zbl 0147.38106)], H. W. Block and J. E. Basu [ibid. 69, 1031-1037 (1974; Zbl 0299.62027)], A. P. Freund [ibid. 56, 971-977 (1961; Zbl 0106.13304)]and F. Proschan and P. Sullo [Reliability and Biometry, SIAM, 423-440 (1974)]distribution of \(Y\) is assumed to be either exponential or gamma. The asymptotic normal (AN) distributions of these estimates are obtained. We present a numerical study for obtaining MLE of \(R\) in all four BVE models when the common stress \((Y)\) is exponentially distributed.