  We study rotating Bose stars, i.e. gravitationally bound clumps of
Bose-Einstein condensate composed of nonrelativistic particles with nonzero
angular momentum $l$. We analytically prove that these objects are unstable at
arbitrary $l\ne 0$ if particle self-interactions are attractive or negligibly
small. In the latter case we calculate the profiles and dominant instability
modes of the rotating stars: numerically at $1 \leq l \leq 15$ and analytically
at $l\gg 1$. Notably, their lifetimes are always comparable to the inverse
binding energies; hence, these objects cannot be considered long-living.
Finally, we numerically show that in models with sufficiently strong repulsive
self-interactions the Bose star with $l=1$ is stable.
