The invention relates to a pressurised fluid flow system for a down-the-hole hammer, comprising principal and auxiliary chambers that exert work on a piston. The auxiliary chambers are formed around respective recesses in the piston and are externally delimited by respective sleeves situated longitudinally in series. A set of supply chambers filled with the pressurised fluid are defined by annular recesses in the outer surface of the piston, for supplying said fluid to the chambers. Supply channels and discharge channels are formed between the outer casing and the sleeves to supply pressurised fluid to the supply chambers by means of outlet holes in the sleeves and to discharge the chambers by means of the discharge holes in the sleeves, respectively. The supply and discharge of the chambers is controlled in a cooperative manner by the piston and the sleeves. A normal-circulation drilling hammer comprising this system is provided.