Abstract
Quasiclassical equations with manifest gauge invariance are discussed in the context of unconventional singlet superconducting states in the static limit. Deviations of the quasiclassical propagator from its equilibrium solutions in the presence of magnetic fields and Hall terms are analysed in terms of a "small" parameter and a formulation developed to first order in "small". A modified quasiclassical propagator is defined to this order that is a solution of a new gauge-invariant Eilenberger-like equation with a normalization condition. A Riccati parametrization with manifest gauge invariance is proposed. Riccati equations are derived to leading order in "small" that are directly applicable to superconducting systems in the presence of magnetic fields.