The vertical and lateral piezoresponse force microscopy were used to perform studies of domain structures in <0 0 1> oriented Pb(Mg1/3Nb2/3)O-3-30%PbTiO3 single crystals with a rhombohedral ferroelectric state. The irregular fingerprinter domain patterns with antiparallel (P) over right arrow ([111])(S)-(P) over right arrow ([(1) over bar(1) over bar(1) over bar])(S) of (P) over right arrow ([(1) over bar 11])(S)-(P) over right arrow ([1 (1) over bar(1) over bar])(S) narrow strip domain patterns with (P) over right arrow ([(1) over bar(1) over bar1])(S)-(P) over right arrow ([11 (1) over bar])(S) polarization orientation and regular, polarization orientation were successfully visualized and determined. The complex, spatial inhomogeneity of ferroelectric domain structures are discussed in terms of local random fields resulting from compositional and charge disorder in PMN-PT relaxor ferroelectric single crystals. (C) 2004 Elsevier B.V. All rights reserved.