A method of operating an abrasive fluid jet cutting system having a high-pressure fluid source (84, 410), an abrasive material source (54, 408, 508, 708), an abrasive fluid jet cutting head (50, 401, 501, 701) configured to generate an abrasive fluid jet from high-pressure fluid supplied by the high-pressure fluid source and abrasive material supplied by the abrasive material source, and an abrasive feed passageway (56, 302, 402, 502, 702) through which the abrasive material from the abrasive material source flows to the abrasive fluid jet cutting head (50, 301, 401, 501, 701),the method comprising: continuously or periodically measuring, throughout at least a portion of a processing operation during which the abrasive fluid jet is discharged from the abrasive fluid jet cutting head (50, 301, 401, 501, 701), a volumetric flow rate of air (Qi, Qi+δ) moving through the abrasive feed passageway at one or more measurement locations; and adjusting the volumetric flow rate of air moving through the abrasive feed passageway (56, 302, 402, 502, 702) based at least in part on said measuring of the volumetric flow rate of the air moving through the abrasive feed passageway (56, 302, 402, 502, 702) at the one or more measurement locations; characterised in that, adjusting the volumetric flow rate of the air moving through the abrasive feed passageway (56, 302, 402, 502, 702) includes one of: introducing air into the abrasive feed passageway at a flow booster location downstream of an abrasive material feed location where the abrasive material enters the abrasive feed passageway from the abrasive material source and upstream of an abrasive material input of the abrasive fluid jet cutting head; withdrawing air from the abrasive feed passageway (56, 402, 502) at a flow dump (420, 520) location downstream of an abrasive material feed location where the abrasive material enters the abrasive feed passageway (56, 402, 502) from the abrasive material source and upstream of an abrasive material input of the abrasive fluid jet cutting head (50, 401, 501). continuously or periodically measuring, throughout at least a portion of a processing operation during which the abrasive fluid jet is discharged from the abrasive fluid jet cutting head (50, 301, 401, 501, 701), a volumetric flow rate of air (Qi, Qi+δ) moving through the abrasive feed passageway at one or more measurement locations; and adjusting the volumetric flow rate of air moving through the abrasive feed passageway (56, 302, 402, 502, 702) based at least in part on said measuring of the volumetric flow rate of the air moving through the abrasive feed passageway (56, 302, 402, 502, 702) at the one or more measurement locations; characterised in that, adjusting the volumetric flow rate of the air moving through the abrasive feed passageway (56, 302, 402, 502, 702) includes one of: introducing air into the abrasive feed passageway at a flow booster location downstream of an abrasive material feed location where the abrasive material enters the abrasive feed passageway from the abrasive material source and upstream of an abrasive material input of the abrasive fluid jet cutting head; withdrawing air from the abrasive feed passageway (56, 402, 502) at a flow dump (420, 520) location downstream of an abrasive material feed location where the abrasive material enters the abrasive feed passageway (56, 402, 502) from the abrasive material source and upstream of an abrasive material input of the abrasive fluid jet cutting head (50, 401, 501). introducing air into the abrasive feed passageway at a flow booster location downstream of an abrasive material feed location where the abrasive material enters the abrasive feed passageway from the abrasive material source and upstream of an abrasive material input of the abrasive fluid jet cutting head; withdrawing air from the abrasive feed passageway (56, 402, 502) at a flow dump (420, 520) location downstream of an abrasive material feed location where the abrasive material enters the abrasive feed passageway (56, 402, 502) from the abrasive material source and upstream of an abrasive material input of the abrasive fluid jet cutting head (50, 401, 501).