  We work out the basic analysis of dynamics near QCD critical point (CP) by
dynamic renormalization group (RG). In addition to the RG analysis by coarse
graining, we construct the nonlinear Langevin equation as a basic equation for
the critical dynamics. Our construction is based on the generalized Langevin
theory and the relativistic hydrodynamics. Applying the dynamic RG to the
constructed equation, we derive the RG equation for the transport coefficients
and analyze their critical behaviors. We find that the resulting RG equation
turns out to be the same as that for the liquid-gas CP except for an
insignificant constant. Therefore, the bulk viscosity and the thermal
conductivity strongly diverge at the QCD CP. We also show that the thermal and
viscous diffusion modes exhibit critical slowing down with the dynamic critical
exponents $z_{\rm thermal}\sim 3$ and $z_{\rm viscous}\sim 2$, respectively. In
contrast, the sound propagating mode shows critical speeding up with the
negative exponent $z_{\rm sound}\sim -0.8$.
