The catalytic properties of six "natural" mutants of the TEM-1 beta-lactamase have been studied in detail, with special emphasis on their activity versus third-generation cephalosporins. On the basis of the recently determined high-resolution structure of the wild-type enzyme, and of the substrates' structures optimized by the AMI quantum chemistry method, we have attempted to explain the influences of the mutations on the substrate profiles of the enzymes. Some of the kinetic results have thus received a satisfactory, semi-quantitative interpretation, especially in the case of single mutations. Analysis of the double mutants proved more hazardous. Extending the comparison to some other class A beta-lactamases showed that similar properties could result from different sequences, supplying an interesting example of convergent evolution within a generally diverging family.