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In brood parasitism, interactions between a parasite and its host lead to a co-evolutionary process called an arms race, in which evolutionary progress on one side provokes a further response on the other side. The host evolves defensive means to reduce the impact of parasitism, while the parasite evolves means to counter the host's defence. To gain insights into the co-evolutionary process of the arms race, a model is developed and analysed, in which the host's defence and the parasite's counterdefence are assumed to be genetically determined. First, the effect of parasite counterdefence on host defence is analysed. I show that parasite counterdefence can critically affect the establishment of host defence, giving rise to three situations in the equilibrium state: The host shows (1) no defence, (2) an intermediate level of defence or (3) perfect defence. Based on these results, the evolution of parasite counterdefence is considered in connection with host defence. It is suggested that the parasite can evolve counterdefence to a certain degree, but once it has established counterdefence beyond this, the host gives up its defence against parasitism provided the defence entails some cost to perform. Dynamic aspects of selection pressure are crucial for these results. Based on these results, I propose a hypothetical evolutionary sequence in the arms race, along which interactions between the host and parasite proceed.