In this paper, we discuss the asymptotic performance of the sequential sign detector for Markovdependent observations. The received signal samples are assumed to be from a stationary, first order Markov process. Both, lower and upper bounds on the average time for detection are computed. A renewal theorem is proved. 1 Introduction It is known that the average sample size of sequential signal detection based on the sequential probability ratio test (SPRT) is the minimum among all the tests that achieve the same probability of decision errors for binary hypothesis [1]. The problem of binary sequential hypothesis testing when the observations are independent and identically distributed has been studied in statistics [1]. Sequential detection also plays an important role in many aspects of signal processing for communication systems [2], [3]. Frequently, quantized observations are used for non-parametric sequential detection [2]. This is an effective solution to the high sensitivity of t...