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Period-luminosity (PL) relations of variable red giants in the Large (LMC)and Small Magellanic Clouds (SMC) are presented. The PL diagrams are plotted inthree planes: logP-K_S, logP-W_{JK}, and logP-W_I. Fourteen PL sequences aredistinguishable, and some of them consist of three closely spaced ridges. Eachof the sequences is fitted with a linear or quadratic function. Thesimilarities and differences between the PL relations in both galaxies arediscussed for four types of red giant variability: OGLE Small Amplitude RedGiants (OSARGs), Miras and Semiregular Variables (SRVs), Long Secondary Periods(LSPs) and ellipsoidal variables. We propose a new method of separating OSARGsfrom non-variable stars and SRVs. The method employs the position in thereddening-free PL diagrams and the characteristic period ratios of thesemultiperiodic variables. The PL relations for the LMC OSARG are compared withthe calculated relations for RGB models along isochrones of relevant ages andmetallicities. We also compare measured periods and amplitudes of the OSARGswith predictions based on the relations valid for less luminous solar-likepulsators. Miras and SRVs seem to follow PL relation of the same slopes in theLMC and SMC, while for LSP and ellipsoidal variables slopes in both galaxiesare different. The PL sequences defined by LSP variables and binary systemsoverlap in the whole range of analyzed wavebands. We put forward new argumentsfor the binary star scenario as an explanation of the LSP variability andelaborate on it further. The measured pulsation to orbital period ratio impliesnearly constant ratio of the star radius to orbital distance, R/A=0.4, as wefind. Combined effect of tidal friction and mass loss enhanced by the low-masscompanion may explain why such a value is preferred.

The Optical Gravitational Lensing Experiment. Period-Luminosity Relations of Variable Red Giant Stars