A method for monitoring the functioning of a compressor, which is switchable into a delivery mode (T F1, T F2, T F3), and which, in the delivery mode, delivers compressed air via a dryer line of a compressed-air preparation unit into at least one main supply line (26, 28), from which multiple supply lines (44, 48, 52, 56, 60) of compressed-air consumer circuits (V21, V22, V23, V24, V25) branch off, wherein a pressure sensor (82, 88, 94) is connected at each of at least some of the supply lines (44, 48, 52, 56, 60), wherein, in the delivery mode of the compressor, a supply pressure p v is detected with the aid of sensors, a pressure gradient derived therefrom is compared to a predefined limiting value, and, depending on the result of the comparison, a warning message or a warning signal is output or not, including the following method steps: a) continuously detecting, with the aid of sensors, the supply pressure p v in a main supply line or in the supply line (44, 48) of at least one compressed-air consumer circuit (V21, V22) provided with a pressure sensor (82, 88), b) continuously calculating the pressure gradients grd_p v of the supply pressure p V from at least two consecutively detected pressure values p v_i, p v_i+1 in each case and the time difference Δt between their detection at least during the delivery mode (T F1, T F2, T F3) of the compressor, c) weighting the pressure gradients grd_p v by division by the particular current drive rotational speed n K of the compressor (grd _ p v_W =grd _ p v / n K) or by the particular current rotational speed-dependent setpoint delivery rate Q soll of the compressor (grd_p V_W =grd _ p V /Q soll), d) comparing the weighted pressure gradients grd_p V_W with a predefined gradient limiting value grd_p G_W, e) outputting a warning message or warning signal if the weighted pressure gradient grd_p V_W has not exceeded the gradient limiting value grd_p G_W within a predefined monitoring time period T M. which is switchable into a delivery mode (T F1, T F2, T F3), and which, in the delivery mode, delivers compressed air via a dryer line of a compressed-air preparation unit into at least one main supply line (26, 28), from which multiple supply lines (44, 48, 52, 56, 60) of compressed-air consumer circuits (V21, V22, V23, V24, V25) branch off, wherein a pressure sensor (82, 88, 94) is connected at each of at least some of the supply lines (44, 48, 52, 56, 60), wherein, in the delivery mode of the compressor, a supply pressure p v is detected with the aid of sensors, a pressure gradient derived therefrom is compared to a predefined limiting value, and, depending on the result of the comparison, a warning message or a warning signal is output or not, including the following method steps: a) continuously detecting, with the aid of sensors, the supply pressure p v in a main supply line or in the supply line (44, 48) of at least one compressed-air consumer circuit (V21, V22) provided with a pressure sensor (82, 88), b) continuously calculating the pressure gradients grd_p v of the supply pressure p V from at least two consecutively detected pressure values p v_i, p v_i+1 in each case and the time difference Δt between their detection at least during the delivery mode (T F1, T F2, T F3) of the compressor, c) weighting the pressure gradients grd_p v by division by the particular current drive rotational speed n K of the compressor (grd _ p v_W =grd _ p v / n K) or by the particular current rotational speed-dependent setpoint delivery rate Q soll of the compressor (grd_p V_W =grd _ p V /Q soll), d) comparing the weighted pressure gradients grd_p V_W with a predefined gradient limiting value grd_p G_W, e) outputting a warning message or warning signal if the weighted pressure gradient grd_p V_W has not exceeded the gradient limiting value grd_p G_W within a predefined monitoring time period T M. a) continuously detecting, with the aid of sensors, the supply pressure p v in a main supply line or in the supply line (44, 48) of at least one compressed-air consumer circuit (V21, V22) provided with a pressure sensor (82, 88), b) continuously calculating the pressure gradients grd_p v of the supply pressure p V from at least two consecutively detected pressure values p v_i, p v_i+1 in each case and the time difference Δt between their detection at least during the delivery mode (T F1, T F2, T F3) of the compressor, c) weighting the pressure gradients grd_p v by division by the particular current drive rotational speed n K of the compressor (grd _ p v_W =grd _ p v / n K) or by the particular current rotational speed-dependent setpoint delivery rate Q soll of the compressor (grd_p V_W =grd _ p V /Q soll), d) comparing the weighted pressure gradients grd_p V_W with a predefined gradient limiting value grd_p G_W, e) outputting a warning message or warning signal if the weighted pressure gradient grd_p V_W has not exceeded the gradient limiting value grd_p G_W within a predefined monitoring time period T M.