Abstract <p>The paper formulates the conditions and proves a theorem on the existence of a Lyapunov-stable steady-state solution to a reaction–diffusion system with slow and fast components in the two-dimensional case. A distinctive feature of the problem formulation is the singular Neumann boundary condition for the fast component. To obtain the result, the asymptotic method of differential inequalities is applied. The results obtained are of practical importance for various applications, for example, for modelling chemical reactions occurring inside rock in oil recovery problems, as well as for developing efficient numerical methods for solving boundary-value problems for elliptic equations.</p>