  Extending prior investigations, we study three of the the four distinct
minimal (4,0) scalar multiplets coupled to (4,0) supergravity. It is found that
the scalar multiplets manifest their differences at the component level by
possessing totally different couplings to the supergravity fields. Only the
SM-I multiplet possesses a conformal coupling. For the remaining multiplets,
terms linear in the world sheet curvature and/or SU(2) gauge field strengths
are required to appear in the action by local supersymmetry.
