  We identify dglas that control infinitesimal deformations of the pairs
(manifold, Higgs bundle) and of Hitchin pairs. As a consequence, we recover
known descriptions of first order deformations and we refine known results on
obstructions. Secondly we prove that the Hitchin map is induced by a natural
L-infinity morphism and, by standard facts about L-infinity algebras, we obtain
new conditions on obstructions to deform Hitchin pairs.
