Abstract <p>In this paper, initial-boundary value problems for a mixed parabolic-hyperbolic equation with characteristic degeneration are set for the first time. A criterion for the uniqueness of solutions is established for each problem.  Solutions to the problems are constructed as sums of series over a system of eigenfunctions of the corresponding one-dimensional spectral problem.  When substantiating the convergence of the constructed series, small denominators arise that complicate the convergence of these series. To prove the uniform convergence of the series, estimates are established for the separation from zero of small denominators with the corresponding asymptotics, which make it possible, under certain conditions with respect to the data of the problem, to prove that the constructed solution belongs to the class of regular solutions.</p>