  We consider dynamics of Bose-Einstein condensates with long-range attractive
interaction proportional to $1/r^b$ and arbitrary angular dependence. It is
shown exactly that collapse of Bose-Einstein condensate without contact
interactions is possible only for $b\ge 2$. Case $b=2$ is critical and requires
number of particles to exceed critical value to allow collapse. Critical
collapse in that case is strong one trapping into collapsing region a finite
number of particles.
  Case $b>2$ is supercritical with expected weak collapse which traps rapidly
decreasing number of particles during approach to collapse. For $b<2$
singularity at $r=0$ is not strong enough to allow collapse but attractive
$1/r^b$ interaction admits stable self-trapping even in absence of external
trapping potential.
