Data on the stability area of trigonal Nd1-xDyxFe3(BO3)(4) phase and the dynamics of labile phases in fluxes based on bismuth trimolibdate are presented. The procedure for crystal nucleation in a thin layer of flux cooled on a platinum rod is reported. Conditions for the growth of Nd1-xDyxFe3(BO3)(4) single crystals on seeds are described. Temperature and field dependences of magnetization and specific heat for single crystals with x=0.1 and 0.25 were measured. It is shown that these single crystals, unlike easy-plane NdFe3(BO3)(4) and easy-axis DyFe3(BO3)(4) antiferromagnets, undergo spontaneous spin-flop phase transitions. Both spontaneous and magnetic field-induced spin reorientations were found to occur in one or several jumps depending on the Nd:Dy ratio in the crystals. (C) 2010 Elsevier B.V. All rights reserved.