We have studied the conformal models WD n ( p ) ,n=3,4,5,..., in the presence of disorder which couples to the energy operator of the model. In the limit of p 1, where p is the corresponding minimal model index, the problem could be analyzed by means of the perturbative renormalization group, with ε-expansion in ε=1/p. We have found that the disorder makes to flow the model WD n ( p ) to the model WD n ( p - 1 ) without disorder. In the related problem of N coupled regular WD n ( p ) models (no disorder), coupled by their energy operators, we find a flow to the fixed point of N decoupled WD n ( p - 1 ) . But in addition we find in this case two new fixed points which could be reached by a fine tuning of the initial values of the couplings. The corresponding critical theories realize the permutational symmetry in a nontrivial way, like this is known to be the case for coupled Potts models, and they could not be identified with the presently known conformal models.