In this paper, the dynamical characteristics of hybrid bi-directional associative memory (BAM) neural networks with constant transmission delays are investigated. Without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions, the Lyapunov functionals are constructed and Halanay-type inequalities are respectively employed to derive the delay-independent sufficient conditions under which the networks converge exponentially to the equilibria associated with temporally uniform external inputs. Some examples are given to illustrate that the results are less conservative and less restrictive than the previously known results.