In this paper, theoretical consideration is made on possibility of subsynchronous resonance (SSR) in longitudinal power systems. Shunt capacitors are used for reactive power compensation in our country, but series capacitors are not used in general. Possibility of SSR is therefore small. However, if power transmis-sion increases, and accordingly, if shunt compensation increases in amount, there is no guarantee that SSR never occur. First, we investigate network impedance viewed from a generator. Its resonant frequencies get lower with increase in transmission power. One of them gets subsynchronous if the power exceeds a value. In this area, there is some possibility of SSR, which is confirmed with the damping property of the generator. The admittance matrix of the load buses are singular at the resonant frequencies. The number of them is equal to the dimension of the matrix. The frequencies are common to all generators but not limited to one particular generator. One of them gets equal to 60 Hz as we increase transmission power. We regard this power as a limit for SSR. However, steady state stability limit is lower than this limit, and steady operation is not possible at the limit. Therefore, it is impossible to enter the area of SSR. Thus we obtain a conclusion that SSR does not occur in shunt compensated systems. However, this property is easily lost if some series compensation is introduced.