this talk is based on my joint work with i. penkov. let g be a simple lie algebra, and $k$ be a reductive subalgebra in $g. a (g,k)-$module $m$ is bounded if it is locally finite over $k$ and the multiplicities of all irreducible finite-dimensional modules in $m$ are uniformly bounded. (two examples from classical representation theory are ladder modules in harish-chandra theory and cuspidal modules in case when $k$ is a cartan subalgebra). i will formulate several general results about bounded modules involving primitive ideals theory and geometry (localization). then i concentrate on the example when $g=b_2$, and $k$ is the principal $sl(2)-$subalgebra, where the complete classification of irreducible simple bounded $(g,k)-$modules is done.