The acylation of furan and 2-methylfuran (2-MF) with acetic acid (AA) and 1-hexanoic acid (HA) was studied over an H-ZSM-5 catalyst. Temperature-programmed desorption (TPD) measurements showed evidence that AA adsorbs strongly at Bronsted sites, with reaction to CO2 and acetone beginning at 523 K, while both furan and 2-MF oligomerize upon adsorption at room temperature. Steady-state, flow-reactor measurements demonstrate that selectivities for the acylation reactions can approach 100% below 523 K when reactions are operated in excess organic acids, with maximum conversion limited by equilibrium. Coking becomes important when the reaction is operated in excess furan or 2-MF and at high reactant concentrations, while ketonization products are observed when the reaction is performed above 523 K. Potential uses for the reactions are discussed.