In this paper, we analyze an empirical model of viscous fingering for three-component, two-phase, first-contact miscible flows. We present the complete range of analytical solutions to secondary and tertiary water-alternating-gas (WAG) floods. An important ingredient in the construction of analytical solutions is the presence of detached (nonlocal) branches of the Hugoniot locus, that is, curves in composition space that satisfy the Rankine-Hugoniot conditions but do not contain the reference state. We illustrate how, in water-solvent floods into a medium with mobile water and residual oil (immobile to water), the solvent front and the water Buckley-Leverett front may interact, resulting in a leading water/solvent shock that is stable to viscous fingering. The analytical solutions explain why in these miscible tertiary floods, oil and solvent often break through simultaneously. We discuss the implications of the new solutions in the design of miscible tertiary floods, such as the estimation of the optimum WAG ratio.