Linearly ordered zero-dimensional compact spaces and linearly ordered continua are investigated with respect to several homogeneity properties. Among the results concerning continua the following may be mentioned: if L is a linearly ordered continuum and S(L) is the circle obtained by glueing the ends of L, then some eight homogeneity properties are equivalent for S(L), in particular, usual homogeneity, 2-homogeneity, strong local homogeneity and homogeneity assuring the similarity of intervals; for instance, the strong local homogeneity means that for open base sets there are homeomorphisms of the space transforming one to the other two arbitrary points of the set and being identity outside the set. Another theorem: if L is homogeneous and antisimilar (there does not exist a self-map f such that \(x<y\) implies \(f(x)>f(y))\), then S(L) is 2- homogeneous but not 3-homogeneous; the n-homogeneity means that each bijection between n-tuples extends to a homeomorphism. The existence of linearly ordered continua which are homogeneous and antisimilar was proved by S. Shelah (1976), and was later confirmed by K. P. Hart and J. van Mill (1985) by \(2^ c\) topologically different examples. These and other theorems of the paper under review are given without proofs following the rule for short notes in the journal in which they are published.