This paper is concerned with the Lagrange exponential stability problem of complex-valued bidirectional associative memory neural networks with time-varying delays. On the basis of activation functions satisfying different assumption conditions, by combining the Lyapunov function approach with some inequalities techniques, different sufficient criteria including algebraic conditions and the condition in terms of LMI are derived to guarantee Lagrange exponential stability of the addressed system, respectively. Moreover, the estimations of different globally attractive sets named the convergence balls are also provided. In the end, the effectiveness and superiority–inferiority of these different results are verified by illustrative examples.