Abstract
We study the covariance properties of fields which according to Mack and Salam's terminology transform as conformal tensors of class Ib and II. A theorem is proved which states the conditions in order that a vector basis of class Ib fields can be turned into a basis of class Ia by subtracting derivatives of the same basic fields. A consequence of this result is a simple rule which allows us to write down all the possible conformal covariant free-field equations. Finally, the conditions for the existence of a unitary inversion operator, as well as the transformation properties of fields under it, have been explicitly determined.
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