The paper presents the method and results of low-frequency noise measurements of modern mid-wavelength infrared photodetectors. A type-II InAs/GaSb superlattice based detector with nBn barrier architecture is compared with a high operating temperature (HOT) heterojunction HgCdTe detector. All experiments were made in the range 1 Hz - 10 kHz at various temperatures by using a transimpedance detection system, which is examined in detail. The power spectral density of the nBn’s dark current noise includes Lorentzians with different time constants while the HgCdTe photodiode has more uniform 1/f - shaped spectra. For small bias, the low-frequency noise power spectra of both devices were found to scale linearly with bias voltage squared and were connected with the fluctuations of the leakage resistance. Leakage resistance noise defines the lower noise limit of a photodetector. Other dark current components give raise to the increase of low-frequency noise above this limit. For the same voltage biasing devices, the absolute noise power densities at 1 Hz in nBn are 1 to 2 orders of magnitude lower than in a MCT HgCdTe detector. In spite of this, low-frequency performance of the HgCdTe detector at ~ 230K is still better than that of InAs/GaSb superlattice nBn detector.