\documentclass{article} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \def\Spin{\text{Spin}} \begin{document} The talk is based on results obtained jointly with V.~Sou\v cek and W.~Wang. Massless field equations in $\mathbb{R}^4$ are studied for a long time. If $S_A$ and $S_{A'}$ denote the two basic spinor representations of the group $\Spin(4)$ then higher spin fields with values in symmetric powers $\odot^k(S_A)$ or $\odot^k(S_A')$ are usually studied. But a~general irreducible $\Spin(4)$ module has a form $\odot^k(S_A)\otimes\odot^l(S_A')$ where $k,l$ are nonnegative integers. What should be the set of equations defining the massless fields with values in a general irreducible $Spin(4)$-module is not generally accepted. The main aim of this talk is to explain that the most appropriate version of these equations are the so-called generalized Cauchy-Riemann equations proposed a long time ago by E. Stein and G. Weiss. They are not, in general, conformally invariant but they are invariant with respect to the action of the group $Spin(4).$ \end{document}