This paper develops the conditions for heterogeneous reactive azeotropy and expands the method described in Okasinski and Doherty (A. I. Ch. E J. 43 (1997) 2227-2238) to cover heterogeneous reactive mixtures, enabling the existence and location of both homogeneous and heterogeneous reactive azeotropes to be determined. Esterification reactions of acetic acid with isopropanol, n-propanol, n-butanol, and n-pentyl alcohol are examined. The results for the n-propanol system, portrayed on a bifurcation diagram, indicate the presence of a heterogeneous minimum-boiling quaternary reactive azeotrope at the value of the reaction equilibrium constant reported in the literature. A heterogeneous reactive azeotrope has not been theoretically predicted before for any mixture. This prediction provides an opportunity for new experiments on heterogeneous, reacting mixtures to determine the validity of the prediction.