  We investigate the critical dynamics of O(N)-symmetric scalar field theories
to determine the critical exponents of transport coefficients as a second-order
phase transition is approached from the symmetric phase. A set of stochastic
equations of motion for the slow modes is formulated, and the long wavelength
dynamics is examined for an arbitrary number of field components, $N$, in the
framework of the dynamical renormalization group within the $\epsilon$
expansion. We find that for a single component scalar field theory, N=1, the
system reduces to the model C of critical dynamics, whereas for $N>1$ the model
G is effectively restored owing to dominance of O(N)-symmetric charge
fluctuations. In both cases, the shear viscosity remains finite in the critical
region. On the other hand, we find that the bulk viscosity diverges as the
correlation length squared, for N=1, while it remains finite for $N>1$.
