Abstract: Water is heated to steam in bayonet tubes and the steam is superheated in bayonet tubes which are heated by helium and which extend from a single tube sheet in which there are no excessively large temperature gradients. Feed water enters the inner tube of a bayonet tube assembly so that it is heated in the annulus between the inner tube and its associated outer tube and then flows into the annular space between the inner and outer tube of a second bayonet tube assembly so that it is heated to steam to leave by the inner tube of the second bayonet tube assembly to then flow into the annular space between the inner and outer tubes of a third bayonet tube assembly to be superheated and leave the third bayonet assembly through the inner tube thereof.