Abstract: The paper deals with the discontinuous oblique derivative problems for second order linear equations of mixed (elliptic-hyperbolic) type with parabolic degeneracy,which include the discontinuous Tricomi problem for Chaplygin equation as a special case.Firstly the formulation and representation of solutions of the above boundary value problems are given,and then the existence of solutions for the above problems is proved,in which the complex analytic method is applied,namely the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used.

Key words: discontinuous oblique derivative problems, second order mixed equations, parabolic degeneracy