Arrays of broadly-selective chemical sensors, also known as electronic noses, have been developed during the past two decades as a low-cost and high-throughput alternative to analytical instruments for the measurement of odorant chemicals. Signal processing in these gas-sensor arrays has been traditionally performed by means of statistical and neural pattern recognition techniques. The objective of this dissertation is to develop new computational models to process gas sensor array signals inspired by coding and learning mechanisms of the biological olfactory system. We have used a neurodynamic model of the olfactory system, the KIII, to develop and demonstrate four odor processing computational functions: robust recovery of overlapping patterns, contrast enhancement, background suppression, and novelty detection. First, a coding mechanism based on the synchrony of neural oscillations is used to extract information from the associative memory of the KIII model. This temporal code allows the KIII to recall overlapping patterns in a robust manner. Second, a new learning rule that combines Hebbian and anti-Hebbian terms is proposed. This learning rule is shown to achieve contrast enhancement on gas-sensor array patterns. Third, a new local learning mechanism based on habituation is proposed to perform odor background suppression. Combining the Hebbian/anti-Hebbian rule and the local habituation mechanism, the KIII is able to suppress the response to continuously presented odors, facilitating the detection of the new ones. Finally, a new learning mechanism based on anti-Hebbian learning is proposed to perform novelty detection. This learning mechanism allows the KIII to detect the introduction of new odors even in the presence of strong backgrounds. The four computational models are characterized with synthetic data and validated on gas sensor array patterns obtained from an e-nose prototype developed for this purpose