The present invention relates to a steam system for a steam cooking appliance. The steam system includes a steam generator (12) and a precipitator (14). The precipitator (14) is arranged above the steam generator (12). The steam generator (12) comprises two vertical heating pipe sections (20; 34). Upper ends of the heating pipe sections (20; 34) are connected to a bottom side of the precipitator (14). Lower ends of the heating pipe sections (20; 34) are connected by a transverse pipe section (20; 36). At least the heating pipe sections (20; 34) are at least partially enclosed by one or more heating elements (22). An inlet pipe (28) is connected to the transverse pipe section (20; 36) at one end and connected or connectable to a water reservoir (16) or water pump (18) at another end. A return pipe (24) is interconnected between the bottom side of the precipitator (14) and the transverse pipe section (20; 36). Further, the present invention relates to a corresponding steam cooking appliance.