Abstract
In this paper we study cosmological dynamics of the phantom as well as non-phantom fields with a linear potential in the presence of a Galileon correction $$ (\partial _\mu \phi \partial ^\mu \phi ) \Box \phi $$ . We show that the Big Crunch singularity is delayed compared to the standard case; the delay crucially depends upon the strength of a Galileon correction. As for the phantom Galileon, $$\rho _{\phi }$$ is shown to grow more slowly compared to the standard phantom delaying the approach of the singularity. In the case, $$V\sim \phi ^n, n>4$$ , Big Rip is also delayed, similar phenomenon is shown to take place for potentials steeper than the exponential.