This review introduces the self-oscillating behavior of two types of nonthermoresponsive polymer systems with Ru catalyst moieties for the Belousov-Zhabotinsky (BZ) reaction: one with a poly-vinylpyrrolidone (PVP) main chain, and the other with a poly(2-propenamide) (polyacrylamide) (PAM) main chain. The amplitude of the VP-based self-oscillating polymer chain and the activation energy for self-oscillation are hardly affected by the initial concentrations of the BZ substrates. The influences of the initial concentrations of the BZ substrates and the temperature on the period of the swelling-deswelling self-oscillation are examined in detail. Logarithmic plots of the period against the initial concentration of one BZ substrate, when the concentrations of the other two BZ substrates are fixed, show good linear relationships. The period of the swelling-deswelling self-oscillation decreases with increasing temperature, in accordance with the Arrhenius equation. The maximum frequency (0.5 Hz) of the poly(VP-co
) gel is 20 times that of the poly(NIPAAm-co
) gel. It is also demonstrated that the amplitude of the volume self-oscillation for the gel has a tradeoff with the self-oscillation period. In addition, this review reports the self-oscillating behavior of an AM-based self-oscillating polymer chain as compared to that of the VP-based polymer chain.