  The two-particle models in de Sitter space-time with time-asymmetric
retarded-advanced interactions are constructed. Particular cases of the
field-type electromagnetic and scalar interactions are considered. The
manifestly covariant descriptions of the models within the Lagrangian and
Hamiltonian formalisms with constraints are proposed. It is shown that the
models are de Sitter-invariant and integrable. An explicit solution of
equations of motion is derived in quadratures by means of projection operator
technique.
