New analytical solutions for the transport of reactive solutes are presented. The solutions apply to solute movement through semi-infinite porous media with adsorption-desorption occurring. Instead of the adsorption-desorption reaction being represented as an instantaneous equilibrium event, a set of exponential time functions were used to provide a time delay before the sorbing solute reaches equilibrium. The models developed in this thesis have the conservative and the linear adsorption solutions of the convective dispersive equation (CDE) as their two extreme limits. In each case, both the flux and the resident concentration solutions were derived. The first set of-solutions represents reactive flow through a one-regime porous media. A "one-term" exponential equation was used to describe the time required to come to adsorption-desorption equilibrium. The flux concentration solution describes the tailing often observed in experimental breakthrough curves. Also, the resident concentration solution exhibits the spreading of solute along the profile that is often observed experimentally. An experiment was performed to evaluate the flux concentration analytical solution. A spike input of lithium solution was applied to a 70 cm long column of undisturbed coarse textured soil, and the soil solution was monitored with solution samplers located at three positions. The analytical solution provided an effective description of the breakthrough data and provided consistent parameter values. A second set of analytical solutions was developed for two-regime porous media based on the mobile-immobile model (MIM). The adsorption-desorption process in the mobile phase is modelled using the equation developed in the previous chapter, unlike previous models that assumed instantaneous equilibrium. Examples of calculated breakthrough curves exhibit subtle changes that might have been previously attributed solely to either physical or chemical phenomena. The final set of analytical solutions was developed for a one-regime porous media. In this example the adsorption-desorption process is modelled by a "two-term" exponential equation. The model parameters allow the reaction rate to rise and fall, approaching a zero rate as equilibrium is established. Examples of calculated breakthrough curves demonstrate bimodal characteristics often attributed solely to the exchange of solute between mobile and immobile regions of structured porous media.