We approach the construct of social presence (SP) from a socio-cultural perspective, taking it as an essential component of computer supported collaborative learning (CSCL) process. We present a qualitative case study in which sixteen student-teachers carried out a computer supported collaborative writing activity in small groups during six weeks. The group activity took place in a blended course at a Bachelor program of Teacher Education. Results allow us to re-define the concept of SP as the concept of SP as the result of constructive and evolutionary discursive group interaction. SP promotes the creation of a community feeling, the maintenance of positive relational dynamics, and the enhancement of self- and collective efficacy in front of the learning task, so that the learning process is supported. The resulting categories correspond to two different axes: individual- versus group-oriented, and task- versus members-oriented. (Contains 4 tables and 6 figures.)