Virtually any electrochemical reaction exhibits temporal or spatial instabilities, such as bistable reaction rates, spontaneous rate oscillations and the formation of propagating potential waves, in some ranges of the external parameters. Most of these instabilities are associated with a negative real faradaic impedance
Z
F
(ω), whereby two cases are distinguished: Either the stationary polarization curve possesses a negative differential resistance, i.e.,
Z
F
(ω = 0) < 0, or
Z
F
is negative only in a certain interval of finite perturbation frequencies ω. The first type of systems may oscillate if a fixed voltage is applied to the cell (i.e., under potentiostatic control), the second class exhibits oscillations under potentiostatic and galvanostatic conditions. Most of the oxidation reactions of small organic molecules belong to the second class. We first discuss general properties of systems falling in either of these two categories. Then we present a survey on temporal and spatial nonlinear phenomena observed in fuel cell relevant electrocatalytic reactions and deduce the reaction steps essential for the instability in the individual reactions.