In rapidly evolving viruses the detection of virally infected cells can possibly be subverted by the production of altered peptides. There are peptides with single amino acid changes that can dramatically change T-cell responses, e.g. a loss of cytotoxic activity. They are still recognized by the T cell, but the signals required for effector function are only partially delivered. Thus, altered peptide presenting cells can act as decoy targets for specific immune responses. The existence of altered peptides in vivo has been demonstrated in hepatitis B and HIV. Using a mathematical model we address the question of how these altered peptides can affect the virus-immune system dynamics, and demonstrate that virus survival is enhanced. If the mutation rate of the virus is sufficient, one observes complex dynamics in which the antagonism acts so as to maintain the viral diversity, possibly leading to the development of a mutually antagonistic network or a continual turnover of escape mutants. In either case the pathogen is able to outrun the immune system. Indeed, sometimes the enhancement is so great that a virus that would normally be cleared by the immune system is able to outrun it.