We report on the intensity dependence of the responsivity in quantum well infrared photodetectors (QWIP). A strong reduction of the responsivity is observed already at small excitation powers for a QWIP with N=4 periods. This nonlinearity is caused by a partial screening of the electric field across the main part of the active region. The intensity dependence is analyzed using a phenomenological approach, which allows us to calculate the nonlinearity from the measured dark current and responsivity. Applying this approach to a background-limited 50 period QWIP, we find that the nonlinearity is already present below 1 mW cm-2, which is less than the thermal background.