Summary: This paper discusses different types of implicit time integration algorithms for the dynamics of spatial beams. The algorithms are based on a form of co-rotational technique which is external to the element. Both end-point and mid-point formulations are presented. The latter can be considered as an ‘approximately energy conserving algorithm’. A new method is described for introducing numerical damping. Finally, some numerical examples are presented in order to illustrate the differences in performance of the different integration schemes.