  In this paper we analyse a certain type of higher derivative gauge theories
which are known to possess BRST symmetry associated with their higher
derivative structure. We first show that these theories are also invariant
under a anti-BRST symmetry and a double BRST symmetry. We then discuss the
invariance of these theories under shift symmetry in the superspace Batalin
Vilkovisky (BV) formalism. We show that these theories are manifestly extended
BRST invariant. However they are only extended anti-BRST invariant on-shell.
