  I study the absorbing-state phase transition in the one-dimensional contact
process with mobile disorder. In this model the dilution sites, though
permanently inactive, diffuse freely, exchanging positions with the other
sites, which host a basic contact process. Even though the disorder variables
are not quenched, the critical behavior is affected: the critical exponents
delta and z, the ratio beta/nu_perp and the moment ratio m= <rho^2>/rho^2 take
values different from those of directed percolation, and appear to vary with
the vacancy diffusion rate. While the survival probability starting from a
single active seed follows the usual scaling, P(t) ~ t^{-delta}, at the
critical point, the mean number of active sites and mean-square spread grow
more slowly than power laws. The critical creation rate increases with the
vacancy density v and diverges at a value v_c < 1. The scaling behavior at this
point appears to be simpler than for smaller vacancy densities.
