  We consider lattice self-avoiding walks and discuss the dynamic critical
behavior of two dynamics that use local and bilocal moves and generalize the
usual reptation dynamics. We determine the integrated and exponential
autocorrelation times for several observables, perform a dynamic finite-size
scaling study of the autocorrelation functions, and compute the associated
dynamic critical exponents $z$. For the variables that describe the size of the
walks, in the absence of interactions we find $z \approx 2.2$ in two dimensions
and $z\approx 2.1$ in three dimensions. At the $\theta$-point in two dimensions
we have $z\approx 2.3$.
