Local Lie groups of local affine transformations are considered. The defining condition
is evaluated, and the connection to the possible different types of the holonomy group (discussed in an earlier paper of the first author and W. Kay
[ibid. 29, No.2, 428-432 (1988; Zbl 0645.53012
)] is established. For non- flat space-times, the maximum dimension of the Lie algebra turns out to be 9. Fixed points and global extensions of affine collineations are discussed.