  In this paper, nonlocal symmetries for the bilinear KP and bilinear BKP
equations are re-studied. Two arbitrary parameters are introduced in these
nonlocal symmetries by considering gauge invariance of the bilinear KP and
bilinear BKP equations under the transformation $f\longrightarrow
fe^{ax+by+ct}$. By expanding these nonlocal symmetries in powers of each of two
parameters, we have derived two types of bilinear NKP hierarchies and two types
of bilinear NBKP hierarchies. An impressive observation is that bilinear
positive and negative KP and BKP hierarchies may be derived from the same
nonlocal symmetries for the KP and BKP equations. Besides, as two concrete
examples, we have deived bilinear B\"acklund transformations for $t_{-2}$-flow
of the NKP hierarchy and $t_{-1}$-flow of the NBKP hierarchy. All these results
have made it clear that more nice integrable properties would be found for
these obtained NKP hierarchies and NBKP hierarchies. Since KP and BKP
hierarchies have played an essential role in soliton theory, we believe that
the bilinear NKP and NBKP hierarchies will have their right place in this
field.
