This paper studies the complexity of sensitivity analysis for optimal and ε-optimal solutions to general 0-1 combinatorial optimization problems with min-max objectives. Van Hoesel and Wagelmans  have studied the complexity of sensitivity analysis of optimal and ε-optimal solutions to min-sum problems, and Ramaswamy et al.  the complexity of sensitivity analysis of optimal solutions to min-max problems. We show that under some mild assumptions the sensitivity analysis of ε-optimal solutions to min-max problems is easy if and only if the original problem is easy. This result is interesting since it immediately applies to a large number of problems, and also because the technique used to prove it is different from the ones used in the related papers (for example, in  and ).