The final cross-linking step of the peptidoglycan synthesis is usually catalyzed by D,D-transpeptidases (PBPs), one of the main targets of beta-lactam antibiotics. Recently, it was shown that these PBPs can be by-passed by a novel class of enzymes, the L,D-transpeptidases (LDts), identified in beta-lactam-resistant bacteria as well as in dormant forms of Mycobacterium tuberculosis. The only beta-lactams enable to inactivate these enzymes belong to the carbapenem class. The beta-lactam ring of this antibiotic family then covalently binds the catalytic cysteine of the LDt. Neither the mechanism of this reaction nor the specificity for carbapenems are yet understood. The aim of the present work is to investigate the acylation mechanism of LDts with carbapenems by NMR. In this context, the first part of this thesis focuses on the current biological understanding of the emergence of this resistance pathway. The second part deals with the NMR principles and the implementations developed to study the structure, thermodynamics and dynamics of LDts. The third part demonstrates that NMR is successful in studying all the steps of the acylation reaction. For this purpose, the LDt apoenzyme, the non-covalent complex with various beta-lactams, and the LDt-carbapenem acylenzyme were thoroughly investigated. The structure of the active site of the Bacillus subtilis apoenzyme was refined with respect to a previous crystallographic study. For the latter and the Enterococcus faecium enzymes, we showed that the carbapenem specificity does not occur at the stage of the non-covalent binding. In contrast to non-covalent interactions, the formation of the covalent bond between LDts and carbapenems induces substantial conformational rearrangement and increased flexibility in the enzyme.