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We consider models with nearest-neighbor interactions and with the set$[0,1]$ of spin values, on a Cayley tree of order $k\geq 1$. We study periodicGibbs measures of the model with period two. For $k=1$ we show that there is noany periodic Gibbs measure. In case $k\geq 2$ we get a sufficient condition onHamiltonian of the model with uncountable set of spin values under which themodel have not any periodic Gibbs measure with period two. We construct severalmodels which have at least two periodic Gibbs measures.

Periodic Gibbs Measures for Models with Uncountable Set of Spin Values on a Cayley Tree