  This paper is devoted to the theory of symplectic instanton bundles on an odd
dimensional projective space ${\mathbb P}^{2n+1}$ with $n\ge 2$. We study the
't Hooft instanton bundles introduced by Ottaviani and a new family of
instanton bundles which generalizes one introduced on ${\mathbb P}^3$
independently by Rao and Skiti. The main result is the determination of the
birational types of the moduli spaces of 't Hooft and of Rao-Skiti instanton
bundles, respectively. Assuming a conjecture of Ottaviani, we show that the
moduli space of all symplectic instanton bundles on ${\mathbb P}^{2n+1}$ with
$n\ge 2$ is reducible.
