In an espresso coffee maker having an espresso brew unit (1) and a coffee outflow duct (18) in fluid-conductive connection with the espresso brew unit via a crema valve (15) and having an end sided coffee outflow (19), no brewed residual coffee should remain in the coffee outflow duct nor leak out, for instance as leakage, through the coffee outflow. In order to avoid this, a return-flow suction unit (21), which is preferably independent except for a drive means, is in fluid-conductive connection with the coffee outflow duct (18) between crema valve (15) and coffee outflow (19), which is automatically activated when a brewing process is finished.