  Griffiths singularities occurring in the unbinding of strongly disordered
heteropolymers are studied. A model with two randomly distributed binding
energies -1 and -v, is introduced and studied analytically by analyzing the
Lee-Yang zeros of the partition sum. It is demonstrated that in the limit v ->
infinity the model exhibits a Griffiths type singularity at a temperature T_G
=O(1) corresponding to melting of long homogeneous domains of the low binding
energy. For finite v >> 1 the model is expected to exhibit an additional,
unbinding, transition at a high temperature T_M=O(v).
