The author studies and compares, using rigorous analytical models, the performances of two algorithms, wavefront and delta -wavefront, suitable for processing an important class of recursive queries, the partially-instantiated transitive closure ones. Such a study reveals, among other findings, that the performance of these algorithms individually as well as relative to each other is strongly dependent on the characteristics of the processed base-relation and, to a lesser degree, the processed query. Moreover, the delta -wavefront has been found to outperform the wavefront with speed advantages reaching several orders of magnitude. >