Abstract: In the study of the Hamiltonian-Hopf bifurcation it is important to estimate the size of the splitting of stable and unstable manifolds which is exponentially small with respect to the bifurcation parameter. It turns out that there exists a universal constant known as Stokes constant, which determines the leading term of an asymptotic formula describing the splitting. The Stokes constant is defined in a problem which depends exclusively on the Hamiltonian at the exact moment of bifurcation — the inner problem. In this talk I will explain the nature of this problem and define the Stokes constant.