This paper studies a class of nonlinearLagrangian algorithms for solving unconstrained minimax problems,which will provide an approach to constructing a concrete andnovel Lagrangian algorithm and simplify the relevant theoryanalysis. A class of nonlinear Lagrangians is constructed and aset of mild conditions on them are proposed to guarantee theconvergence theory of the corresponding algorithms. The unifiedconvergence analysis framework for the class of algorithms isestablished. It is shown that the sequence solutions obtained bythe class of algorithms are Q-linearly convergent when thecontrolling parameter is less than a threshold under someassumptions and the error bounds of the sequence solutions areobtained at the same time. The properties of dual problemframework based on the unified nonlinear Lagrangians are analyzed, which theclassical Lagrangian lacks. Furthermore, it is presented that theproposed class of nonlinear Lagrangians contains fourwell-known nonlinear Lagrangians for unconstrained minimaxproblems appearing in the literatures. At last, numerical results for ten typicaltest problems are reported, based on the four nonlinear Lagrangians in the proposed class.