Normal contact of two elastic spherical bodies with functionally graded coatings is considered.Materials can be isotropic or transversely-isotropic.Elastic modnli of each coating vary with depth according to arbitrary functions.Using integral transformation technique the problem is reduced to the solution of integral equation.Using the approximation of the kernel transform by the product of fractional quadratic functions the approximated solution of the dual integral equation is constructed in analytical form.The influence of the elastic (ratio of the effective elastic modulus of the coatings and substrates) and geometrical (ratio of the thicknesses of the coatings,relative thickness of one coating) parameters of the problem on the contact stresses and radius of the contact area are studied.Numerical examples illustrated obtained results are provided.The contact problems for piezoelectric half-space with functionally-graded coating with mixed electrical and mechanical boundary conditions are also studied.