Comparison of the theory of orthogonal polynomials in a single complex variable2 with that of orthogonal polynomials in two real variables3 readily suggests the primary facts with regard to orthogonal polynomials in two complex variables. Such facts may be enumerated without details of demonstration. The extension from two to four real dimensions, however, naturally increases the variety of the phenomena to be noted, and after the first stages of analogy leads to developments which call for more sustained examination. The purpose of this paper is to give an introduction to the theory in two complex variables, with emphasis on certain features of it which are not brought out in the presentations that have come to the writer's attention.4