For a Markov chain X={Xi, i=1, 2, …, n} with the state space {0, 1}, the random variable S:=∑i=1nXi is said to follow a Markov binomial distribution. The exact distribution of S, denoted $\mathcal{L}S$ , is very computationally intensive for large n (see Gabriel [Biometrika 46 (1959) 454–460] and Bhat and Lal [Adv. in Appl. Probab. 20 (1988) 677–680]) and this paper concerns suitable approximate distributions for $\mathcal{L}S$ when X is stationary. We conclude that the negative binomial and binomial distributions are appropriate approximations for $\mathcal{L}S$ when Var S is greater than and less than $\mathbb{E}S$ , respectively. Also, due to the unique structure of the distribution, we are able to derive explicit error estimates for these approximations.