We analyze the dynamical system defined by a universe filled with a barotropic fluid plus a scalar field with modified kinetic term of the form L = F (X) - V (phi). After a suitable choice of variables that allows us to study the phase space of the system we obtain the critical points and their stability. We find that they reduce to the ones defined for the canonical case when F (X) = X. We also study the field energy conditions to have a nonsingular bounce.