On conformal covariance of spinor field equations

It is shown that the equation γ^μ_?μψ (χ) = 0 is covariant with respect to proper conformal transformations if the four-component spinor field ψ(χ) is a Cartan conformal semispinor of the first or second kind. If, instead, ψ is a Dirac spinor, then no less than two such equations are needed in a covariant field theory where the conformal group may be represented linearly. Some consequences are outlined.