  We study the Batalin-Vilkovisky master equation for both open and closed
string field theory with special attention to anomalies. Open string field
theory is anomaly free once the minimal coupling to closed strings induced by
loop amplitudes is considered. In closed string field theory the full-fledged
master equation has to be solved order by order in perturbation theory. The
existence of a solution implies the absence of anomaly. We briefly discuss the
relation of the iterative process of solution to methods used in the first
quantized formalism and comment on some possible non-perturbative corrections.
