Nowadays, the Internet network system serves as a platform for communication, transaction, and entertainment, among others. This communication system is characterized by terrestrial and Satellite components that interact between themselves to provide transmission paths of information between endpoints. Particularly, Satellite Communication providers' interest is to improve customer satisfaction by optimally exploiting on demand available resources and offering Quality of Service (QoS). Improving the QoS implies to reduce errors linked to information loss and delays of Internet packets in Satellite Communications. In this sense, according to Internet traffic (Streaming, VoIP, Browsing, etc.) and those error conditions, the Internet flows can be classified into different sensitive and non-sensitive classes. Following this idea, this work aims at finding new Internet traffic classification approaches to improving the QoS. Machine Learning (ML) and Deep Learning (DL) techniques will be studied and deployed to classify Internet traffic. All the necessary elements to couple an ML or DL solution over a well-known Satellite Communication and QoS management architecture will be evaluated. To develop this solution, a rich and complete set of Internet traffic is required. In this context, an emulated Satellite Communication platform will serve as a data generation environment in which different Internet communications will be launched and captured. The proposed classification system will deal with different Internet communications (encrypted, unencrypted, and tunneled). This system will process the incoming traffic hierarchically to achieve a high classification performance. Finally, some experiments on a cloud emulated platform validates our proposal and set guidelines for its deployment over a Satellite architecture.