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Neisseria gonorrhoeae plasmids can mediate high-level antimicrobial resistance. The emergence of clinical isolates producing plasmid β-lactamases that can hydrolyze cephalosporins, the mainstay treatment for gonorrhea, may be a serious threat. In this work, N. gonorrhoeae strains producing plasmid-mediated broad- and extended-spectrum β-lactamases (ESBLs) were obtained in vitro, and their viability and β-lactam antibiotic susceptibility were studied. Artificial pblaTEM-1 and pblaTEM-20 plasmids were constructed by site-directed mutagenesis from a pblaTEM-135 plasmid isolated from a clinical isolate. Minimum inhibitory concentration (MIC) values for a series of β-lactam antibiotics, including benzylpenicillin, ampicillin, cefuroxime, ceftriaxone, cefixime, cefotaxime, cefepime, meropenem, imipenem, and doripenem, were determined. The N. gonorrhoeae strain carrying the pblaTEM-20 plasmid exhibited a high level of resistance to penicillins and second–fourth-generation cephalosporins (MIC ≥2 mg/L) but not to carbapenems (MIC ≤0.008 mg/L). However, this strain stopped growing after 6 h of culture. The reduction in viability was not associated with loss of the plasmid but can be explained by the presence of the plasmid itself, which requires additional reproduction costs, and to the expression of ESBLs, which can affect the structure of the peptidoglycan layer in the cell membrane. Cell growth was mathematically modeled using the generalized Verhulst equation, and the reduced viability of the plasmid-carrying strains compared to the non-plasmid-carrying strains was confirmed. The cell death kinetics of N. gonorrhoeae strains without the pblaTEM-20 plasmid in the presence of ceftriaxone can be described by a modified Chick–Watson law. The corresponding kinetics of the N. gonorrhoeae strain carrying the pblaTEM-20 plasmid reflected several processes: the hydrolysis of ceftriaxone by the TEM-20 β-lactamase and the growth and gradual death of cells. The demonstrated reduction in the viability of N. gonorrhoeae strains carrying the pblaTEM-20 plasmid probably explains the absence of clinical isolates of ESBL-producing N. gonorrhoeae.