  In the paper we formulate and derive the family blowup formula of family
Seiberg-Witten invariants. The formula has been used in the enumerative
application of counting singular curves on algebraic surfaces. We first give a
topological derivation of the formula by using family index theorem. Then we
define the algebraic (family) Seiberg-Witten invariants for algebraic surfaces
and then give an algebraic derivation of the family blowup formula for the
algebraic family Seiberg-Witten invariants.
