jats:titleAbstract</jats:title>jats:pWe introduce and develop a theory of orthogonality with respect to Sobolev inner products on the real line for sequences of functions with a tridiagonal, skew‐Hermitian differentiation matrix. While a theory of such Ljats:sub2</jats:sub> ‐orthogonal systems is well established, Sobolev orthogonality requires new concepts and their analysis. We characterize such systems completely as appropriately weighted Fourier transforms of orthogonal polynomials and present a number of illustrative examples, inclusive of a Sobolev‐orthogonal system whose leading jats:italicN</jats:italic> coefficients can be computed in  operations.</jats:p>