<p>The aim of this paper is to investigate two types of Levitin–Polyak well-posedness for split equilibrium problems. We establish the binary gap function of split equilibrium problems and present sufficient and necessary conditions to characterize two types of Levitin–Polyak well-posedness of split equilibrium problems. Further, based on the upper semicontinuity of the approximate solution sets, we propose equivalent characterizations of the type I Levitin–Polyak well-posedness. Under certain conditions, we prove that split equilibrium problems are type I Levitin–Polyak well-posed if and only if the solution sets are nonempty and compact in finite-dimensional spaces. Numerical examples are provided to illustrate the proposed findings.</p>