Abstract <p> The existence of a unique solution to a nonlocal conjugation problem for a third-orderpartial differential equation of mixed parabolic-hyperbolic type is established. In the upperhalf-plane, the characteristic equation has a triple root, while in the lower half-plane, it has onesimple root and two multiple ones. By applying the order reduction method, Green’s andRiemann’s functions, and the method of integral equations, the problem is equivalently reduced toa nonlocal problem with an integral condition imposed on the trace of the unknown function alongthe type-change line of the equation. This, in turn, is reduced to solving a Fredholm integralequation of the second kind, the solvability of which is proven using the method of successiveapproximations. The solution in the parabolic part of the domain is constructed using Green’sfunction, whereas in the hyperbolic part, the Riemann function method is employed, reducing theproblem to a two-dimensional Volterra integral equation of the second kind. Examples areprovided.</p>