Recently, blends and composites of biodegradable polymers have been developed to replace petroleum-based plastics. Polybutylene adipate terephthalate and polyhydroxybutyrate are polymers that have received much attention due to their interesting mechanical properties. Polyhydroxybutyrate is highly biodegradable. However, polybutylene adipate terephthalate is quite difficult to biodegrade under environmental conditions, and only a few microorganisms are known with this capability. In this work, two fungi isolated from soil were characterized regarding their ability to biodegrade polybutylene adipate terephthalate and polyhydroxybutyrate/polybutylene adipate terephthalate films. The polymers were the sole carbon and energy source. The biodegradation assays were performed in monoculture and coculture. Biodegradation was assessed in solid and liquid media. Clear zone formation was monitored during incubation in agar plates containing the polymers. Film weight loss was measured after incubations in a liquid salt medium. The consumption of oxygen was also monitored to confirm biodegradation. These fungi could efficiently biodegrade polyhydroxybutyrate/polybutylene adipate terephthalate films to similar extents. Remarkably, after 14 days of incubation, isolate 7 (assigned to Aspergillus pseudoflectus) achieved 40.7% (wt) biodegradation and isolate 9 (assigned to Purpureocillium lilacinum) 43.4% (wt). The coculture biodegraded 40.6% (wt). Polybutylene adipate terephthalate biodegradation was far more challenging, and in 287 days, isolates 9 and 7 achieved 41.2% and 30.2% respectively. This is the first study reporting the biodegradation of polyhydroxybutyrate/polybutylene adipate terephthalate films by aerobic mesophilic fungi. These fungi are promising candidates for the development of polybutylene adipate terephthalate biodegradation technologies and bioremediation strategies to clean up environmental plastic contamination.