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This paper examines a mathematical model for the coevolution of parasite virulence and host resistance under a multilocus gene-for-gene interaction. The degrees of parasite virulence and host resistance show coevolutionary cycles for sufficiently small costs of virulence and resistance. Besides these coevolutionary cycles of a longer period, multilocus genotype frequencies show complex fluctuations over shorter periods. All multilocus genotypes are maintained within host and parasite classes having the same number of resistant/virulent alleles and their frequencies fluctuate with approximately equally displaced phases. If either the cost of virulence or the number of resistance loci is larger then a threshold, the host maintains the static polymorphism of singly (or doubly or more, depending on the cost of resistance) resistant genotypes and the parasite remains universally avirulent. In other words, host polymorphism can prevent the invasion of any virulent strain in the parasite. Thus, although assuming an empirically common type of asymmetrical gene-for-gene interaction, both host and parasite populations can maintain polymorphism in each locus and retain complex fluctuations. Implications for the red queen hypothesis of the evolution of sex and the control of multiple drug resistance are discussed.