  Starting from the classic definitions of local resolvent set and spectrum of
a linear bounded operator on a Banach space, we introduce the local resolvent
set and spectrum, the local space and the single-valued extention property of a
family of linear bounded operators on a Banach space. Keeping the analogy with
the classic case, we extend some the known results from the case of a linear
bouded operator to the case of a family of linear bounded operators on a Banach
space.
