  We show that instanton bundles of rank $r\le 2n-1$, defined as the cohomology
of certain linear monads, on an $n$-dimensional projective variety with cyclic
Picard group are semistable in the sense of Mumford-Takemoto. Furthermore, we
show that rank $r\le n$ linear bundles with nonzero first Chern class over such
varieties are stable. We also show that these bounds are sharp.
