The non-additive binary hard particle mixture is characterized by a collision parameter between unlike hard particles that is not the arithmetic mean of the two pure component collision diameters. Instead, sigma(12) = (sigma(11) + sigma(22)) (1 + Delta)/2, where sigma(12) is the collision diameter between species 1 and 2 and Delta is a non-additivity parameter in which Delta > -1 (Delta = 0 corresponds to the additive mixture). For mixtures in which repulsive forces are mostly responsible for the observed behavior, the binary non-additive hard particle mixture provides a useful model for examining the thermophysical properties of a wide class of real fluid mixtures. To extend further the range of applicability of these mixtures, another layer of complexity can be considered by including potential interactions that exist past contact which themselves may also be defined as non-additive. For example, the well depth of the interaction of unlike species can be defined as epsilon(12) = delta\epsilon(11)epsilon(22)\(1/2), where delta is another non-additivity parameter which may take on any real value (note that Delta = 0 and delta = 1 correspond to the Lorentz-Berthelot mixing rules). To gain insight into these complicated mixtures in higher dimensions, we consider the one-dimensional non-additive binary hard rod mixture with various attractive interactions. We generate the exact thermophysical properties of these mixtures, including a general form of the equation of state. Similarly, we also determine the radial distribution functions, g (ij)(r), using the exactly known nearest-neighbor probability density distributions. Such relations enable one to determine the effects of the various non-additive parameters on the properties of the mixtures. (C) 2004 Elsevier B.V. All rights reserved.