  In $2000$, Colliot-Th\'el\`ene and Poonen showed how to construct algebraic
families of genus one curves violating the Hasse principle. Poonen explicitly
constructed an algebraic family of genus one cubic curves violating the Hasse
principle using the general method developed by Colliot-Th\'el\`ene and
himself. The main result in this paper generalizes the result of
Colliot-Th\'el\`ene and Poonen to arbitrarily high genus hyperelliptic curves.
More precisely, for $n > 5$ and $n \not\equiv 0 \pmod{4}$, we show that there
is an algebraic family of hyperelliptic curves of genus $n$ that is
counterexamples to the Hasse principle explained by the Brauer-Manin
obstruction.
