Staphylococcus aureus causes a broad range of infections and is often characterized by multidrug resistance (MDR). Treatment of staphylococcal infections is further complicated by the ability of bacterium to form biofilms protecting it against antimicrobial agents and the immune system. The use of bacteriophages is one of the promising strategies for combating the bacteria showing MDR and biofilm formation activity. The study aimed to assess the effects of the lytic phages vB_SauM515A1 (genus Kayvirus, family Herelleviridae) and vB_SauP-436A (genus Rosenblumvirus, family Rountreeviridae) on biofilms of the S. aureus clinical strains. The study involved 20 strains of eight sequence types, among which 45% (9/20) belonged to MRSA, and 35% (7/20) showed MDR. All the strains demonstrated the ability to form biofilms, and 65% (13/20) were strong biofilm producers. Genes of the icaADBC operon responsible for synthesis of polysaccharide intercellular adhesin were found in genomes of all samples. The exposure of planktonic bacterial cells to bacteriophages showed that 70% (14/20) of strains were sensitive to phage vB_SauM-515A1 and 50% (10/20) were sensitive to phage vB_SauP-436A. Furthermore, the 24-h treatment of biofilms of sensitive strains with phage vB_SauM-515A1 led to the biofilm biomass increase in 64.3% (9/14) of cases, while phage vB_SauP-436A, on the contrary, significantly reduced the quantity of biofilm in 40% (4/10) of strains. The results obtained highlight the ambiguity of interaction between bacteriophages and S. aureus biofilms and suggest the need for further research aimed at optimizing phage therapy targeting the biofilm-forming strains.