The so-called Mild Cognitive Impairment (MCI) or cognitive loss appears in a previous stage before Alzheimer's Disease (AD), but it does not seem sufficiently severe to interfere in independent abilities of daily life, so it usually does not receive an appropriate diagnosis. Its detection is a challenging issue to be addressed by medical specialists. This work presents a novel proposal based on automatic analysis of speech and disfluencies aimed at supporting MCI diagnosis. The approach includes deep learning by means of Convolutional Neural Networks (CNN) and non-linear multifeature modelling. Moreover, to select the most relevant features non-parametric Mann-Whitney U-testt and Support Vector Machine Attribute (SVM) evaluation are used.