In this paper, we consider anti-periodic solutions of the following BAM neural networks with multiple delays on time scales: $${{x^Delta_i(t)=-a_i(t)e_i(x_i(t))+{sumlimits^m_{j=1}}c_{ji}(t)f_j(y_j(t-{ au}_{ji}))+I_i(t),atop y^Delta_j(t)=-b_j(t)h_j(y_j(t))+{sumlimits^n_{i=1}}d_{ij}(t)g_i(x_i(t-{delta}_{ij}))+J_j(t),}$$ where i = 1, 2, ..., n,j = 1, 2, ..., m. Using some analysis skills and Lyapunov method, some sufficient conditions on the existence and exponential stability of the anti-periodic solution to the above system are established.