This article studies the dynamics of ratio-dependent models for continuous bioreactors involving interactions between predator, prey, and a limiting substrate. Ratio-dependent models, for which the growth rate of predator is a function of the ratio of prey to predator abundance, have recently received growing attention and were shown to exhibit more interesting behavior than the classical (strictly) prey-dependent models. It is shown that in addition to predicting areas of predator washout and areas of total washout, the studied examples of ratio-dependent models predict areas for which the species coexist either at steady state or in oscillatory mode for any initial population values. The studied models also predict a unique feature for which the interacting species can coexist or wash out depending on their initial values. The objective of this article is to study in some detail this interesting behavior that makes ratio-dependent models better candidates in predicting predator-prey interactions in real biological life.