Stokes’ discontinuities occur in the asymptotic approximation of functions defined by integrals or differential equations and dependent on a large complex parameter \(\lambda\). Usually several asymptotic estimates are available in different sectors of the complex \(\lambda\)-plane. At the border lines of the sectors, usually called Stokes lines, the change in the approximations is not always smooth; the jumps may be exponentially large. If the expansion is truncated near its least term, the change may be smooth, and can be described in terms of an error function. This new interpretation introduces an interesting development in the theory of asymptotic expansions. The author uses the formalism of Dingle to describe the phenomenon, and he gives numerical illustrations for Dawson’s integral and Airy functions.