  The purpose of this paper is to study the behaviour of sequences of
generalised monopoles with a uniform bound on a certain L2-norm. We focus on
the case that the target hyperKahler manifolds are Swann bundles. In
3-dimensional case, suppose that there exists an open submanifold Y' such that
the hyperKahler potential along the monopoles has a uniform lower bound over
Y'. Then we show that there exist convergent subsequences of generalised
monopoles over any compact subset of Y'. Under similar assumptions, the same
conclusion holds for the generalised harmonic spinors in dimension four.
