A method for monitoring the leakage of a compressed air system of a motor vehicle, which compressed air system comprises a compressed air supply installation, a compressor connected thereto on the input side, and a plurality of compressed air consumer circuits (V21, V22, V23, V24, V25) connected thereto on the output side, wherein a supply pressure (p v) is detected by sensors, a pressure gradient derived from this supply pressure is compared with a predetermined limit value, and a warning signal is output depending on the comparison result, the method comprising the following method steps: a) continuously detecting the supply pressure (p v) by sensors by means of a pressure sensor in a main supply line (26, 28) or in the supply line of at least one compressed air consumer circuit in a predefined time cycle (Δt), b) continuously calculating the pressure gradients (grd_p v) of the supply pressure (p v) from at least two successively detected pressure values (p v_i, p v_i+1) and the time difference (Δt) between the detection thereof at least during the delivery pauses (T FP1, T FP2, T FP3) of the compressor, c) comparing the determined pressure gradients (grd_p v) with a predefined gradient limit value (grd_pc), d) outputting a warning signal when the pressure gradient (grd_p v) within a predefined monitoring time period (T M), which comprises a plurality of delivery pauses (T FP1, T FP2, T FP3) of the compressor, has not exceeded the gradient limit value (grd_pc), characterized in that pressure fluctuations of the supply pressure (p v), which are attributed to thermodynamic effects occurring in the compressed air consumer circuits, are eliminated by the calculated values of the pressure gradient (grd_p v) being low-pass filtered for a set time interval (T A) after an identified sharp drop in the supply pressure (p v), and/or the calculation of the values of the pressure gradient (grd_p v) or the comparison of the pressure gradient (grd_p v) with the gradient limit value (grd_p g) does not take place for a set time interval (T A) after an identified sharp drop in the supply pressure (p v). a) continuously detecting the supply pressure (p v) by sensors by means of a pressure sensor in a main supply line (26, 28) or in the supply line of at least one compressed air consumer circuit in a predefined time cycle (Δt), b) continuously calculating the pressure gradients (grd_p v) of the supply pressure (p v) from at least two successively detected pressure values (p v_i, p v_i+1) and the time difference (Δt) between the detection thereof at least during the delivery pauses (T FP1, T FP2, T FP3) of the compressor, c) comparing the determined pressure gradients (grd_p v) with a predefined gradient limit value (grd_pc), d) outputting a warning signal when the pressure gradient (grd_p v) within a predefined monitoring time period (T M), which comprises a plurality of delivery pauses (T FP1, T FP2, T FP3) of the compressor, has not exceeded the gradient limit value (grd_pc), characterized in that pressure fluctuations of the supply pressure (p v), which are attributed to thermodynamic effects occurring in the compressed air consumer circuits, are eliminated by the calculated values of the pressure gradient (grd_p v) being low-pass filtered for a set time interval (T A) after an identified sharp drop in the supply pressure (p v), and/or the calculation of the values of the pressure gradient (grd_p v) or the comparison of the pressure gradient (grd_p v) with the gradient limit value (grd_p g) does not take place for a set time interval (T A) after an identified sharp drop in the supply pressure (p v). pressure fluctuations of the supply pressure (p v), which are attributed to thermodynamic effects occurring in the compressed air consumer circuits, are eliminated by the calculated values of the pressure gradient (grd_p v) being low-pass filtered for a set time interval (T A) after an identified sharp drop in the supply pressure (p v), and/or the calculation of the values of the pressure gradient (grd_p v) or the comparison of the pressure gradient (grd_p v) with the gradient limit value (grd_p g) does not take place for a set time interval (T A) after an identified sharp drop in the supply pressure (p v).