We investigate the enclosing control problem of heterogeneous multi-agent systems composed of first-order and second-order dynamical agents in fixed directed topologies. Firstly, four effective control protocols are proposed for the two cases in which the system contains both first-order dynamical leaders and second-order dynamical followers, second-order dynamical leaders and first-order dynamical followers, respectively. Then, by using algebraic graph theory, matrix theory and stability analysis tools, the criteria for the above two types of heterogeneous multi-agent systems to achieve enclosing control are obtained through the system transformation method or the error vector construction method. Finally, the effectiveness of the proposed protocols is further verified by simulations.