  Enhanced Yang-Baxter operators give rise to invariants of oriented links. We
expand the enhancing method to generalized Yang-Baxter operators. At present
two examples of generalized Yang-Baxter operators are known and recently three
types of variations for one of these were discovered. We present the definition
of enhanced generalized YB-operators and show that all known examples of
generalized YB-operators can be enhanced to give corresponding invariants of
oriented links. Most of these invariants are specializations of the polynomial
invariant $P$. Invariants from generalized YB-operators are multiplicative
after a normalization.
