  Two links are called link-homotopic if they are transformed to each other by
a sequence of self-crossing changes and ambient isotopies. The notion of
link-homotopy is generalized to spatial graphs and it is called
component-homotopy. The link-homotopy classes were classified by Habegger and
Lin through the classification of the link-homotopy classes of string links. In
this paper, we classify colored string links up to colored link-homotopy by
using the Habegger-Lin theory. Moreover, we classify colored links and spatial
graphs up to colored link-homotopy and component-homotopy respectively.
