  Using changes of probability measure developed by \mbox{Grama} and Haeusler
(Stochastic Process.\ Appl., 2000), we obtain two generalizations of the
deviation inequalities of Lanzinger and Stadtm\"{u}ller (Stochastic Process.\
Appl., 2000) and Fuk and Nagaev (Theory Probab. Appl., 1971) to the case of
martingales. Our inequalities recover the best possible decaying rate of
independent case. Applications to linear regressions and weak invariance
principles for martingales are provided.
