Background and objective: Acinetobacter baumannii (A. baumannii) is an important nosocomial pathogen that not only possesses intrinsic resistance to many classes of antibiotics, but is also capable of rapidly developing antimicrobial resistance during treatment. The aim of this study was to determine the characteristics of resistance of A. baumannii strains to β-lactams and other tested antibiotics, to evaluate the associations between the phenotypes of resistance to β-lactams and other tested antibiotics, and to evaluate the changes in antibiotic resistance of A. baumannii strains over 5 years by comparing the periods of 2016–2017 and 2020–2021. Materials and methods: A total of 233 A. baumannii strains were isolated from different clinical specimens of patients treated at the Hospital of Lithuanian University of Health Sciences in 2016–2017 (n = 130) and 2021–2022 (n = 103). All clinical cultures positive for A. baumannii were analyzed. The type of β-lactamase was detected by phenotypic methods using ESBL plus AmpC screen disk tests and the combination meropenem disk test. Results: In both periods, all A. baumannii strains were resistant to ciprofloxacin; resistance to carbapenems, piperacillin/tazobactam, gentamicin, and tobramycin was noted in more than 80% of strains. A comparison of two periods showed that the percentages of A. baumannii strains producing two or three types of β-lactamases were significantly greater in 2021–2022 than in 2016–2017 (94.2% and 5.8% vs. 17.7% and 2.3%, respectively, p < 0.001). Isolates producing two or three types of β-lactamases were more often resistant to tigecycline, tetracycline, and doxycycline than strains producing one type of β-lactamase (p < 0.001). Conclusions: The frequency of isolation of A. baumannii strains producing two different types of β-lactamases (AmpC plus KPC, AmpC plus ESBL, or ESBL plus KPC) or three types of β-lactamases (AmpC, KPC, and ESBL) and the resistance rates to ampicillin/sulbactam, tigecycline, tetracycline, and doxycycline were significantly greater in 2020–2021 as compared with 2016–2017. The production of two or three types of β-lactamases by A. baumannii strains was associated with higher resistance rates to tetracyclines.