In the talk, we will outline the proofs that Helly groups and CB-groups are biautomatic. Helly groups are the groups acting geometrically on Helly graphs and CB-groups are the groups acting geometrically on graphs with convex balls. Helly groups represent a common generalization of hyperbolic groups, CAT(0) cubical groups, graphical C(4)-T(4) small cancellation groups, swm-groups, and some other classes of groups. CB-groups generalize weakly systolic and systolic groups. Both proofs of biautomiaticity use a result of ´Swi¸atkowski (2006) providing sufficient conditions of biautomaticity in terms of local recognition and bicombing and a construction of normal clique paths in the graph on which the group acts. The normal clique paths in Helly graphs and in CB-graphs are defined using different properties of such graphs. In case of CB-graphs, our construction generalizes the construction of Januszkiewicz and ´Swi¸atkowski (2006) for systolic groups. The talk is based on the following papers.