If X is a life distribution with finite mean then its mean residual life function (MRLF) is defined by M(x)=E[X−x|X>x]. It has been found to be a very intuitive way of describing the aging process. Suppose that M1 and M2 are two MRLFs, e.g., those corresponding to the control and the experimental groups in a clinical trial. It may be reasonable to assume that the remaining life expectancy for the experimental group is higher than that of the control group at all times in the future, i.e., M1(x)⩽M2(x) for all x. Randomness of data will frequently show reversals of this order restriction in the empirical observations. In this paper we propose estimators of M1 and M2 subject to this order restriction. They are shown to be strongly uniformly consistent and asymptotically unbiased. We have also developed the weak convergence theory for these estimators. Simulations seem to indicate that, even when M1=M2, both of the restricted estimators improve on the empirical (unrestricted) estimators in terms of mean squared error, uniformly at all quantiles, and for a variety of distributions. [Copyright &y& Elsevier]