  We construct generalized additional symmetries of a two-component BKP
hierarchy defined by two pseudo-differential Lax operators. These additional
symmetry flows form a Block type algebra with some modified(or additional)
terms because of a B type reduction condition of this integrable hierarchy.
Further we show that the D type Drinfeld-Sokolov hierarchy, which is a
reduction of the two-component BKP hierarchy, possess a complete Block type
additional symmetry algebra. That D type Drinfeld-Sokolov hierarchy has a
similar algebraic structure as the bigraded Toda hierarchy which is a
differential-discrete integrable system.
