Silicon lowers the Neel temperature, T-N, and enhances the paramagnetic characteristic of gamma-Fe-Mn alloy, which results in a reduction of the stability of austenite and in the anomalous increase of electrical resistivity, rho, below T-N becoming stronger, i.e. the anomalous rho below TN increases rapidly with increasing silicon content. The gamma reversible arrow epsilon transformation occurs during cooling and heating, but gamma --> epsilon martensitic transformation is suppressed below about 240 K, probably due to the epsilon phase transfer from paramagnetic to antiferromagnetic state. The rho(T) changes steeply, accompanying the Neel transition and the gamma reversible arrow epsilon transformation. Silicon increases the electrical resistivity and the magnetic susceptibility, chi, of gamma-Fe-Mn alloy, and the epsilon phase obviously increases the electrical resistivity of Fe-Mn-Si alloys. The relation between the Neel transition, gamma --> epsilon martensitic transformation and shape memory effect (SME), are discussed.