Molecules having covalent catalytic activity are identified by panning synthetic and semisynthetic combinatorial libraries on solid phase suicide substrates. In an alternative mode, mechanism-based inhibitors or affinity labels may substituted for the suicide substrate. Covalent catalysts within the combinatorial library form covalent conjugates with the suicide substrate, mechanism-based inhibitor, or affinity label. Covalent conjugates are immobilized by attachment to the suicide substrate to solid phase and are easily separated from unconjugated elements of the combinatorial library by stringent washing. Combinatorial libraries employing phagemid-display are particularly preferred since such phagemids include genetic material for identifying and amplifying conjugated catalysts. Covalent catalysts obtainable by this method include, inter alia, molecules having esterolytic activity, aldol condensation activity, .beta.-lactamase activity, glycosidase activity, RNase activity, and proteolytic activity.