It has been established that a polymer-coated SH-SAW sensor on 36° rotated Y-cut LiTaO3 is a very sensitive platform for direct liquid-phase chemical sensing. In this work, two partially selective coatings, poly(epichlorohydrin) and Polyurethane are investigated for the detection of organophosphate pesticides (phosmet and parathion) in aqueous solutions. Moreover, in order to meet the need for sensitive and selective chemical detection systems, novel signal processing techniques are employed in the detection process. First, the sensor response is modeled in terms of all relevant contributions (mass loading and viscoelasticity) using a state-space approach. Transient information, often unique to a given analyte/coating pair, is then extracted using nonlinear estimation theory and used to distinguish between chemical species, explain observed sensor responses, and decrease detection time. A detection limit in the ppb range can be achieved from the current experimental measurements.