MPEJ Volume 7, No. 2, 19 pp. Received: Jun 13, 2000. Revised: Oct 3, 2001. Accepted: Oct 9, 2001. M. Abadi: Exponential approximation for hitting times in mixing processes ABSTRACT: We present bounds for the error of the exponential approximation of the first occurrence time of a rare event in a stationary stochastic process with a finite alphabet with the $\alpha$-mixing property with a summable function $\alpha$ or with a general $\phi$-mixing property. We prove a lower bound for this error in terms of the measure of the cylinder and an upper bound as a function of the measure of the cylinder plus the decay of correlation of the process.