Recent observations reveal that plasmas in cometary tails contain charged dust grains of positive and negative polarities. Our objective here is to show that such a two-component dusty plasma supports dust-Langmuir and dust-acoustic waves. The latter in the nonlinear regime propagate in the form of localized negative potentials. The role of large amplitude potential structures for trapping the positive dust grains and for the formation of dust layers of opposite polarity is discussed.