  In renormalizable theories, we define equal-time commutators (ETC'S) in terms
of the equal-time limit and investigate its convergence in perturbation theory.
We find that the equal-time limit vanishes for amplitudes with the effective
dimension $d_{\em eff} \leq -2$ and is finite for those with $d_{\em eff} =-1$
but without nontrivial discontinuity. Otherwise we expect divergent equal-time
limits. We also find that, if the ETC's involved in verifying an Jacobi
identity exist, the identity is satisfied.
  Under these circumstances, we show in the Yang-Mills theory that the ETC of
the $0$ component of the BRST current with each other vanishes to all orders in
perturbation theory if the theory is free from the chiral anomaly, from which
we conclude that $[\, Q\,,\,Q\,]=0$, where $Q$ is the BRST charge. For the case
that the chiral anomaly is not canceled, we use various broken Ward identities
to show that $[\, Q\,,\,Q\,]$ is finite and $[\,Q\,,\,[\, Q\,,\,Q]\,]$ vanishes
at the one-loop level and that they start to diverge at the two-loop level
unless there is some unexpected cancellation mechanism that improves the degree
of convergence.
