This paper considers the stability of a valve amplifier which has an oscillatory circuit in the grid and in the anode circuit. An exact condition for stability is obtained for circuits which have no resistance, and it is shown that when both circuits have the same natural frequency instability is then impossible if the anode inductance exceeds μ times the grid circuit inductance. This condition is believed to be new; in practice it is unnecessarily severe, but it is believed that stability should be sought by increasing the anode inductance and the grid circuit capacity. The stability of circuits which have resistance is too cumbersome to express generally, but it is discussed on broad principles; the stability and amplification of multistage amplifiers are also considered briefly. The following papers should be compared with the present one.