We introduce the self-linking number of a smooth closed curve alpha : S-1 -
-> R-n with respect to a 3-dimensional vector bundle over the curve, provid
ed that some regularity conditions are satisfied. When n = 3, this construc
tion gives the classical self-linking number of a closed embedded curve wit
h non-vanishing curvature [5]. We also look at some interesting particular
cases, which correspond to the osculating or the orthogonal vector bundle o
f the curve.