Background: Klebsiella pneumoniae is an opportunistic pathogen that causes a wide range of infections worldwide. The emergence and spread of multidrug-resistant clones requires the implementation of novel therapeutics, and phages are a promising approach. Results: In this study, two Klebsiella phages, KpTDp1 and KpTDp2, were isolated from wastewater samples in Tunisia. These phages had a narrow host range and specifically targeted the hypervirulent K2 and K28 capsular types of K. pneumoniae. Both phages have double-stranded linear DNA genomes of 49,311 and 49,084 bp, respectively. Comparative genomic and phylogenetic analyses placed phage KpTDp2 in the genus Webervirus, while phage KpTDp1 showed some homology with members of the genus Jedunavirus, although its placement in a new undescribed genus may be reconsidered. The replication efficiency and lytic ability of these phages, combined with their high stability at temperatures up to 70 °C and pH values ranging from 3.5 to 8.2, highlight the potential of these phages as good candidates for the control of hypervirulent multidrug-resistant K. pneumoniae. Methods: Phage isolation, titration and multiplicity of infection were performed. The stability of KpTDp1 and KpTDp2 was tested at different pH and temperatures. Genomic characterization was done by genome sequencing, annotation and phylogenetic analysis. Conclusions: The ability of KpTDp1 and KpTDp2 to lyse one of the most virulent serotypes of K. pneumoniae, as well as the stability of their lytic activities to pH and temperature variations, make these phages promising candidates for antibacterial control.