  Andrew Rajah posed at the Loops'11 Conference in Trest, Czech Republic, the
following conjecture: Is every variety of loops that satisfies Moufang's
theorem contained in the variety of Moufang loops? This paper is motivated by
that problem. We give a partial answer to this question and present two types
of Steiner loops, one that satisfies Moufang's theorem and another that does
not, and neither is Moufang loop.
