Chat conversations and other types of online communication environments are widely used within CSCL educational scenarios. However, there is a lack of theoretical and methodological background for the analysis of collaboration. Manual assessing of non-moderated chat discussions is difficult and time-consuming, having as a consequence that learning scenarios have not been widely adopted, neither in formal education nor in informal learning contexts. An analysis method of collaboration and individual participation is needed. Moreover, computer-support tools for the analysis and assessment of these conversations are required. In this paper, we start from the "polyphonic framework" as a theoretical foundation suitable for the analysis of textual and even gestural interactions within collaborative groups. This framework exploits the notions of dialogism, inter-animation and polyphony for assessing interactions between participants. The basics of the polyphonic framework are discussed and a systematic presentation of the polyphonic analysis method is included. Then, we present the "PolyCAFe" system, which provides tools that support the polyphonic analysis of chat conversations and online discussion forums of small groups of learners. Natural Language Processing (NLP) is used in order to identify topics, semantic similarities and links between utterances. The detected links are then used to build a graph of utterances, which forms the central element for the polyphonic analysis and for providing automatic feedback and support to both tutors and learners. Social Network Analysis is used for computing quantitative measures for the interactions between participants. Two evaluation experiments have been undertaken with "PolyCAFe". Learners find the system useful and efficient. In addition to these advantages, tutors reflecting on the conversation can provide quicker manual feedback.