It was recently shown that, in the solution of smooth constrained optimization problems by sequential programming (SQP), the Maratos effect can be prevented by means of a certain nonmonotone (more precisely, four-step monotone) line search. Using a well known transformation, this scheme can be readily extended to the case of minimax problems. It turns out however that, due to the structure of these problems, one can use a simpler scheme. Such a scheme is proposed and analyzed in this paper. It is also shown that a three-step monotone (rather than four-step monotone) line search, with a relaxed decrease requirement, can be used without losing the theoretical convergence properties. Numerical experiments indicate a significant advantage of the proposed line search over the (monotone) Armijo search.