  In a previous paper conformal gravity was derived by means of a precise
action principle on the hypercone in the conformal space. Here it is shown that
the same technique used to construct conformal spin two theory as represented
by linear conformal gravity may also be used for the construction of conformal
higher spin theories. The basic ingredients in these constructions are gauge
invariant field strengths (curvatures). In fact, their very existence as
manifestly conformal fields requires the present conformal theory. The general
form of the actions for the free theories on the hypercone are given. In
spacetime these actions are shown to be expressed in terms of squares of
generalized Weyl tensors. Conformal spin three and four are calculated
explicitly. The theories are proposed to be equivalent to the free theories
given by Fradkin and Linetsky. Since the equations are of order 2s a consistent
quantization is difficult to achieve but might exist. Interactions are expected
to exist and is the motivation behind this approach.
