  We show how the well-known classical field equations as Einstein and
Yang-Mills ones, which arise as the conformal invariance conditions of certain
two-dimensional theories, expanded up to the second order in the formal
parameter, can be reformulated as Generalized/formal Maurer-Cartan equations
(GMC), where the differential is the BRST operator of String theory. We
introduce the bilinear operations which are present in GMC, and study their
properties, allowing us to find the symmetries of the resulting equations which
will be naturally identified with the diffeomorphism and gauge symmetries of
Einstein and Yang-Mills equations correspondingly.
