Direct perturbation theory (DPT) for relativistic effects is generalized to the case of a set of near-degenerate strongly interacting states. This situation, where the standard approach breaks down, is quite common in atoms and especially in molecules. We introduce a new partitioning of the Dirac equation and apply the Moller-Bloch approach. An effective Schrodinger-like equation within a nonrelativistic model space of near-degenerate states is derived. The effective Hamiltonian and metric operators are expressed with the help of a Moller wave operator Omega, which generates the complete four-component Dirac wave function from the nonrelativistic Schrodinger wave function in the finite model space. The corresponding Bloch equation can be solved numerically in a basis set to infinite order by iteration. Also explicit formulas are derived for different orders of H-eff and S-eff. They can be used to determine the relativistic energies to different orders either directly by diagonalization, or by a perturbation approach.