  We carry out a comprehensive study of the dynamics of large-scale
perturbations in quintessence scenarios. We model the contents of the Universe
by a perfect fluid with equation of state w_f and a scalar field Q with
potential V(Q). We are able to reduce the perturbation equations to a system of
four first-order equations. During each of the five main regimes of
quintessence field behaviour, these equations have constant coefficients,
enabling analytic solution of the perturbation evolution by eigenvector
decomposition. We determine these solutions and discuss their main properties.
