Аннотация:The paper studies two-dimensional modal logics with additional connectives(so-called Segerberg squares) and can be regarded as a continuation of Shehtman (Russian Mathematical Surveys, 67(4):721–778, 2012). It gives a new simpler proof of the finite model property of minimal Segerberg squares using bisimulation games.It proves the square finite model property for Segerberg squares of polymodal T andD. It also constructs a faithful embedding of Segerberg squares in the equationaltheory of relation algebras.