This paper presents some theoretical results of a general study of the interaction between surface gravity waves and a steady current Assuming irrotational flow and a second order Stokes wave motion, the main objects of the paper have been a To present a simple graphical method for the computation of the wave length m a current field b To introduce the concept of the mean energy level for a periodic wave motion with a steady current superimposed c To utilize this for the calculation of the "current-wave set-down" for a two-dimensional motion with a constant discharge over a gently sloping bottom d To present a complete set of conservation equations for the case considered under point c e To present graphs and tables for the variation in length and height of wave for the case considered under point c No experimental results are presented.