  For quadratic forms over fields of characteristic different from two, there
is a so-called Vishik criterion, giving a purely algebraic characterization of
when two quadratic forms are motivically equivalent. In analogy to that, we
define Vishik equivalence on quasiliner $p$-forms. We study the question
whether Vishik equivalent $p$-forms must be similiar. We prove that this is not
true for quasilinear $p$-forms in general, but we find some families of totally
singular quadratic forms (i.e., of quasilinear $2$-forms) for which the
question has positive answer.
