  The BKP hierarchy has a two-component analogue (the 2-BKP hierarchy).
Dispersionless limit of this multi-component hierarchy is considered on the
level of the $\tau$-function. The so called dispersionless Hirota equations are
obtained from the Hirota equations of the $\tau$-function. These dispersionless
Hirota equations turn out to be equivalent to a system of Hamilton-Jacobi
equations. Other relevant equations, in particular, dispersionless Lax
equations, can be derived from these fundamental equations. For comparison,
another approach based on auxiliary linear equations is also presented.
