For the creation of powerfully catalytic antibodies, the technique of reactive immunization solves the problem inherent in immunization with transition-state analogs (TSAs), namely, that many interesting target reactions are multistep reactions, with multiple transition states, and thus in general, no single analog can adequately simulate all the transition states along the reaction path. In contrast, immunization with chemically reactive antigens such as phosphonylating agents, which phosphonylate B-cells during the immune response, produces antibodies that have been "trained" to recognize, bind, and stabilize all the actual transition states involved in the phosphonylation reaction. Therefore, catalytic antibodies have been selected by the immune system on the basis of their capacity to stabilize any number of transition states that occur during the target reaction. Somewhat surprisingly, phosphonolysis catalysts generated in this way commonly also catalyze esterolysis reactions. Esterolysis reactions should pass through transition states with a roughly tetrahedral disposition of ligands about a central carbon atom, while phosphonolysis reactions should pass through transition states with a roughly trigonal-bipyramidal disposition of ligands about a central phosphorus atom. These two divergent transition-state geometries suggest that the same active site should have difficulty recognizing and stabilizing both kinds of transition state. The observations thus indicate a puzzling form of "cross-reactivity" toward transition states. A possible explanation arises from evidence that at least some nucleophilic displacements at phosphorus do not pass through a trigonal-bipyramidal adduct, with a bond-formation transition state preceding it and a bond-fission transition state succeeding it. Instead a single transition state is traversed in which both bond-formation and bond-fission occur simultaneously. Such a concerted-reaction transition state should have two weak, partial bonds to phosphorus, one for formation of the nucleophile-P bond and one for fission of the P-leaving group bond. In a stepwise reaction through an intermediate, only one bond is partial and weak in each of the two transition states. The concerted-reaction transition state, with two weak bonds to phosphorus, may be more easily compressed, expanded, and otherwise distorted because of the lower force constants associated with partial bonds; particularly distortions of angles involving the two partial bonds should require relatively low energies. This may lend a high level of flexibility to phosphonolysis transition states, allowing them to be accommodated within an active site (or a range of active sites) with strong catalytic stabilization. Included among these active sites may be a majority that can also stabilize esterolysis transition states. Indeed many of the target esterolysis reactions studied to date may occur through a single concerted-reaction transition state rather than through separate transition states before and after a tetrahedral intermediate. Thus, the esterolysis transition states may also be highly flexible. Finally, flexibility present in germline antibodies may be specifically preserved in reactive immunization. The high flexibility of both kinds of ligands and of the antibody combining site may then account for the catalytic "cross-reactivity" of these antibodies.