  Using the notion of spectral flow, we suggest a simple approach to various
asymptotic problems involving eigenvalues in the gaps of the essential spectrum
of self-adjoint operators. Our approach uses some elements of the spectral
shift function theory. Using this approach, we provide generalisations and
streamlined proofs of two results in this area already existing in the
literature. We also give a new proof of the generalised Birman-Schwinger
principle.
