We report on specific heat and inelastic neutron scattering experiments of the heavy electron system Ce(Ru 1− x Rh x ) 2Si 2 ( x ⩽ 0.03). A spin density wave (SDW) transition was observed for 0.03 < x<0.4. We applied the self consistent renormalization (SCR) theory for the low Rh concentration region ( x ⩽ 0.03) of this system, and well explained the temperature dependence of the specific heats. We obtained the dynamical susceptibilities χ( q, ω) in the q- and ω-space by inelastic neutron scattering experiments. We discuss the effect of antiferromagnetic spin fluctuations on the dynamical properties of Ce(Ru 1− x Rh x ) 2Si 2 near the magnetic instability point on the basis of the SCR theory.