Kinetics of the initial stages of the bulk polymerization of 4-acetoxybenzoic acid (ABA) and 6-acetoxy-2-naphthoic acid (ANA) were investigated. A method to analyze the kinetics by measuring the amount of evolved acetic acid trapped in a sodium hydroxide solution by titrimetry was developed. All polymerizations followed second-order reaction kinetics up to 70% conversion. Two kinetic regions were observed in the homopolymerization of ABA and copolymerization of ABA and ANA in the melt, visible by a break in the time-conversion curve. The average degree of polymerization at the change of mechanism point from a homogeneous to a heterogeneous system was 3.5. The time of the change in mechanism and the reaction rate were dependent on the temperature and the initial concentration ratio of ABA and ANA used in the polymerization. The higher the temperature and the concentration of ABA, the earlier the break takes place and the faster the reaction proceeds. The corresponding reaction rate constants and activation energies were obtained.