Presently, conditions ensuring the validity of bootstrap methods for the sample mean of (possibly heterogeneous) near epoch dependent (NED) functions of mixing processes are unknown. A0501n purpose of this paper is thus to establish the validity of the bootstrap in this context, extending the applicability of bootstrap methods to a class of processes broadly relevant for applications in economics and finance. The results apply to the moving blocks bootstrap of Künsch (1989) and Liu and Singh (1992) as well as to the stationary bootstrap of Politis and Romano (1994). In particular, the consistency of the bootstrap variance estimator for the sample mean is shown to be robust against heteroskedasticity and dependence of unknown form. The first order asymptotic validity of the bootstrap approximation to the actual distribution of the sample mean is also established in this heterogeneous NED context.