Within a model of quasi-two dimensional electron system interacting via on site Coulomb potential we study theoretically the collective behavior of the field induced spin density waves (FISDW) in Bechgaard salts. In a FISDW there are two gapless modes associated with the spin rotation around the external magnetic field and the sliding of the FISDW. These gapless modes cancel exactly the anomaly due to the modification of the quasi-particle spectrum below Tc in the correlation functions like <[S3, S3]>, <[n, n]> and <[jx, jx]> where S3, n and jx are the spin parallel to the external field, the electron density and the electron current parallel to the chain direction. The low frequency behavior of these correlation functions are unchanged at the FISDW transition when the quasi-particle damping is ignored. However, the rotational symmetry of the spin is broken by the dipole energy which gives rise to a small energy gap in the longitudinal spin wave spectrum below Tc, which is accessible to the electron spin resonance. Furthermore the translational invariance of the SDW is in general broken by impurities and/or crystalline defects, which gives rise to the SDW pinning. Then the resulting expression of <[n, n]> and <[jx, jx]> resembles to those in a CDW in quasi-one dimensional conductors. Therefore we predict similar nonlinear conductivity in the presence of electric field and electromechanical effects as found in the CDW systems.