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This thesis describes studies of unitary currents flowing through two different potassium (K) channels present in sarcolemmal vesicles of the frog, Rana temporaria. The ATP-regulated K-channel is described first and the results are divided into three parts. Firstly, ATP applied to the cytoplasmic face of a membrane patch closes the channels in a dose-dependent fashion. Different nucleotides and other metabolic substances are used in order to find chemicals which can substitute for ATP or which regulate its effect. Secondly, the permeability properties of the channel are described. Ion flux is non-independent. Rubidium (Rb) is permeant, and anomalous mole-fraction behaviour is demonstrated in mixtures of K+and Rb+. The final part investigates the kinetic properties of the channel. Both voltage and ATP affect the rate constants regulating transitions between closed and open states of the channel. In particular, ATP causes the channel to occupy a very long-lived closed state. Block of the channel by tetraethylammonium (TEA) ions applied to either membrane surface is described as well. Block by external TEA+ is very fast and it is suggested that the channel cannot close when blocked. The block by internal TEA+ is slower and some evidence of voltage dependency is seen. The delayed rectifier K-channel is investigated. The first of two parts describes Rb+ permeability of the channel and its effect on open and closed times. The Hodgkin-Huxley model of the channel is questioned by the very different times of occupancy of closed states and differing voltage dependencies of the steps leading to opening of the channel. The second part describes block of the channel by externally applied TEA+ and the blocking reaction is shown to be very fast and voltage dependent.