We propose a structured multisignature scheme which is based on a modified ElGamal signature scheme and analyze its security. The structure takes into account the order of the signers. With serial structures, different signing orders produce different multisignatures. In contrast, with parallel structures the multisignatures are independent of the signing order. Our structured multisignatures can deal with structures which are composed of serial and parallel signing orders. We give reductions for the security of the proposed scheme, and for the specified order of the signers in the serial and mixed cases.