  We study the deformation of the holomorphic-Higgs pair. The holomorphic-Higgs
pair is a pair of a complex manifold and a Higgs bundle over it. We introduce
the differential graded Lie algebra (DGLA) which comes from the deformation. We
derive the Maurer-Cartan equation which governs the deformation of the
holomorphic-Higgs pair, construct the Kuranishi family of it, and prove its
local completeness.
