Lie methods of integration of second-order ODEs are generalized for systems of second-order ODEs.
Using the known classification of real non-similar four-dimensional Lie algebras in the space of three variables we construct general forms of systems which are invariant with respect to ganarators of each of these algebras. It is demonstrated that the symmetries of obtained systems can be used for their integration.
The integration algorithm for arbitrary systems of two second-order ODEs with four symmetries is suggested.