 Besides the studies concerning preservation of metaproperties by fibring mentioned above, the semantics of fibred logics is not so easy to determine from the semantics of the components. That is, there is no natural correspondence between the models of the component logics and the class of models which characterizes the least logic in the mixed language which extends simultaneously the given logics, that is, their fibring. This question is far from being simple: for instance, in Marcelino and Caleiro 2017a it was shown that the act of fibring two logics, each of one being characterized by a single finite matrix, can produce a logic which is uncharacterizable by a single matrix (even infinite). In Marcelino and Caleiro 2017b a first step towards the solution of this problem was given, by characterizing the semantics of unconstrained fibring of logics presented by means of nondeterministic matrix semantics.  Nondeterministic matrices (or Nmatrices) generalize logical matrices by allowing the connectives to be interpreted by multivalued truth-functions instead of ordinary truth-functions. Nmatrices were formally introduced in Avron and Lev 2001 (see also Avron and Lev 2005) to provide a semantical account for logics uncharacterizable by a single finite matrix. However, the use of Nmatrices for logics was already considered by several authors (Rescher 1962; Ivlev 1973, 1985, 1988 and Kearns 1981 in the context of modal logics; and Crawford and Etherington 1998). By using two different notions of product of Nmatrices, in Marcelino and Caleiro 2017b it is shown that the disjoint fibring of two propositional logics, each of one presented by a single Nmatrix, is characterized by a single Nmatrix obtained from the given ones by using these products. This encompasses the fibring of logics presented by matrices, since every logical matrix is, in particular, a non-deterministic matrix.