  We study the Cucker-Smale (C-S) flocking systems involving both singularity
and noise. We first show the local strong well-posedness for the stochastic
singular C-S systems in a general setting, in which the communication weight
$\psi$ is merely locally Lipschitz on $(0,\infty)$ and has lower bound (could
be negative). Then, for the special case that the singularity at origin is of
higher order (i.e. $\alpha\ge1$), we establish the global well-posedness by
showing the collision-avoidance in finite time, provided the initial
distribution has finite moment. Finally, we will study the large time behavior
of the solution when $\psi$ is of zero lower bound, and provide the emergence
of conditional flocking and unconditional flocking respectively in stochastic
sense.
