Asthma is an inflammatory condition of the peripheral (small) airways. It is the most prevalent chronic respiratory disease in children. Reliable and patient-friendly instruments and methods are required to help pulmonologists accurately detect Asthma and Small Airway Impairment (SAI) with acceptable clinical accuracy, specificity and sensitivity. It has been shown that Impulse Oscillometry System (IOS) parameters as well as parameter estimates of equivalent electrical circuit models provide useful indicators of lung function. Two respiratory models known as extended RIC (eRIC) and augmented RIC (aRIC) models have emerged which offer advantages over earlier models. This research aims to analyze IOS data acquired from children during pre- and post-bronchodilation conditions, as well as evaluate the eRIC and aRIC model estimated parameters to determine which ones are better to differentiate between constricted and non-constricted lung conditions. It is also the first attempt to establish reference values for North American Hispanic and Anglo children and to find correlations between IOS features and eRIC and aRIC model parameters.