RNA virus evolution is generally considered to be highly unpredictable, but tests of determinism in the evolution of competing populations during viral infections have not been performed. Here we study the fate of two closely related evolving quasispecies of vesicular stomatitis virus, by determining the relative concentration of a wild-type clone and a surrogate marked virus subclone (MARM-C) upon extensive competitive replication in a constant cell culture environment. A highly predictable nonlinear behaviour of the two competing populations was found. In addition, the presence of critical points, which are defined as points from which viral competitions may follow different trajectories, has been documented. Critical points were reached after nearly constant periods of time. The dynamics of relative fitness values for both competing populations were calculated during the replication passages. Concomitant with expected fitness gain of both competing viral populations (which follow the Red Queen hypothesis) a tendency for the MARM-C to gain less fitness than the wild-type was observed. Although fitness variations were noisy, this tendency was seen in all evolutionary replicas. Thus, despite the stochastic process of mutation that leads to a continuous generation of mutant genomes during RNA virus replication, a nonlinear, nearly deterministic evolutionary behaviour has been observed. It is proposed that such a behaviour is mediated by a low-pass filter (averaging of mutational noise signals) due to competitive selection among variants.