The notion of an S-homotopy group of an arbitrary chamber system over a set \(\Delta_ n\) where \(S\leq 2^{\Delta_ n}\) has been introduced by J. Tits in his work on local characterizations of buildings. Any Coxeter complex can be viewed as a chamber system \(\Sigma\). In this case, S can be viewed as a linear graph with as set vertices \(\Delta_ n\). Basicly by choosing a suitable maximal tree in the chamber graph ch(\(\Sigma)\) of \(\Sigma\), the S-homotopy group \(\pi^ S(\Sigma)\) can be computed explicitly for a lot of S’s and \(\Sigma\) ’s. When S contains no minimal circuit of length \(>3\), then \(\pi^ s(\Sigma)\) is a free group. In a more recent paper, the author proves the converse too. This result also holds for buildings. The rank of these groups can be computed.