  We define the universal sl3-link homology, which depends on 3 parameters,
following Khovanov's approach with foams. We show that this 3-parameter link
homology, when taken with complex coefficients, can be divided into 3
isomorphism classes. The first class is the one to which Khovanov's original
sl3-link homology belongs, the second is the one studied by Gornik in the
context of matrix factorizations and the last one is new. Following an approach
similar to Gornik's we show that this new link homology can be described in
terms of Khovanov's original sl2-link homology.
