  In this paper we establish the existence of monads on multiprojective spaces
$X=\mathbb{P}^{2n+1}\times\mathbb{P}^{2n+1}\times\cdots\times\mathbb{P}^{2n+1}$.
We prove stability of the kernel bundle which is a dual of a generalized
Schwarzenberger bundle associated to the monads and prove that the cohomology
vector bundle is simple, a generalization of instanton bundles. Next we
construct monads on $\mathbb{P}^{a_1}\times\cdots\times\mathbb{P}^{a_n}$ and
prove stability of the kernel bundle and that the cohomology vector bundle is
simple. Lastly, we construct the morphisms that establish the existence of
monads on $\mathbb{P}^1\times\cdots\times\mathbb{P}^1$.
