Cough is the most common symptom of several respiratory diseases. It is a defense mechanism of the body to clear the respiratory tract from foreign materials inhaled accidentally or produced internally by infections. The identification of wet and dry cough is an important clinical finding, aiding in the differential diagnosis. Wet coughs are more likely to be associated with bacterial infections. At present, the wet/dry decision is based on the subjective judgment of a physician, during a typical consultation session. It is not available for long term monitoring or in the assessment of treatment efficacy. In this paper we address these issues and develop fully automated technology to classify cough into `Wet' and `Dry' categories. We propose novel features and a Logistic regression-based model for the classification of coughs into wet/dry classes. The performance of the method was evaluated on a clinical database of pediatric and adult coughs recorded using a bed-side non-contact microphone. The sensitivity and specificity of the classification were obtained as 79±9% and 72.7±8.7% respectively. These indicate the potential of the method as a useful clinical tool for cough monitoring, especially at home settings.