The nonradiative photoexcitation energy transfer in systems of densely packed PbS quantum dots (QDs) of different sizes is studied by steady-state and transient photoluminescence (PL) spectroscopy. It is shown that F枚rster resonance energy transfer dominates the process and dramatically changes the dynamics of the photoexcited charge carriers as compared to systems of noninteracting QDs. As a result, the initially quite different lifetimes of the lowest energy electronic states of the QDs approach each other and increase up to values characteristic for the long-lived luminescence of the QD donors. This slowdown effect in the PL decay in densely packed systems of PbS QDs with optical transitions in the near-infrared may find applications in solar energy harvesting.