W e consider a kinematical system of n Euclidean 3-dimen- sional spaces Sj(i = l,2,3,...,n) moving with respect to each other and containing a differentiable line-system of one dual parameter T = t 4* e t*. The case of t* = 0 is considered as a special case. In sections II and III, for the analysis of the relative motion of the system we derive the properties of general dual motions in matrix algebra över the ring of dual numbers.