The authors analyze a boundary version of Morera's theorem for classical domains. The starting point is Nagel and Rudin's result claiming that, if a function \(f\) is continuous on the boundary of a ball in \(\mathbb C^N\) and \[ \int_0^{2\pi}f(\psi(e^{i\varphi}, 0\dots, 0)) e^{i\varphi} d\varphi = 0 \] for all (holomorphic) automorphisms \(\psi\) of the ball, then \(f\) can be extended holomorphically onto the ball. In the article under review, the authors generalize the above assertion to the case of classical domains, replacing the boundary of the domain with its Shilov boundary (the skeleton). The proof is based on ideas different from those of \textit{A. Nagel} and \textit{W.~Rudin} [Duke. Math. J. 43, No. 4, 841-865 (1976; Zbl 0343.32017)] and enables us to prove Nagel and Rudin's theorem in the case of a ball.