An agent can usually hold a very large amount of beliefs. However, only a
small part of these beliefs is used at a time. Efficient operations for belief
change should affect the beliefs of the agent locally, that is, the changes
should be performed only in the relevant part of the beliefs.  In this paper
we generalize the operations for belief change defined by Hansson. 
We obtain representation theorems for the operations
based on a generic consequence operator $C$ that does not need to be
classic. We define a local consequence operator that only considers the
relevant part of a belief base and show that this operator can be used to
define local versions of the operations for belief change.