This is the second of two papers comparing relational network theory with transformational theory. In Reich 1970b we defined some basic nodes and compared relational network theory with a subset of transformational theory which is commonly acknowledged to be linguistically inadequate. In this paper we shall review the types of problems which context-free phrase-structure grammars cannot adequately handle. We shall then show that each of these problems occurs in that portion of English grammar which is concerned with the English auxiliaries; thus a good test of any proposed grammatical theory is whether or not it can be used to describe a grammar of the auxiliaries in an acceptable way. Finally, we shall describe in detail a relational network grammar of the auxiliaries and attempt to demonstrate that relational network theory passes this test.