  We consider the problem of deforming simultaneously a pair of given
structures. We show that such deformations are governed by an L-infinity
algebra, which we construct explicitly. Our machinery is based on Th. Voronov's
derived bracket construction.
  In this paper we consider only geometric applications, including deformations
of coisotropic submanifolds in Poisson manifolds, of twisted Poisson
structures, and of complex structures within generalized complex geometry.
These applications can not be, to our knowledge, obtained by other methods such
as operad theory.
