Consideration of the ternary phase relationships between components of the XYB2O6 berates, where X = Na, K, Rb, or Cs and Y = No or Ta, suggest that the conditions for their optimal single-crystal growth can be determined from predicted pseudo-binary phase diagrams. Several compounds have been synthesised on the basis of the predicted Nb2O5: Rb(K)(2)B4O7 pseudo-binary systems and single crystals of KNbB2O6 (KNB) and RbNbB2O6 (RNB) grown for the first time by spontaneous nucleation from their self-fluxes. Larger crystals of RNB were grown and these also had a better optical quality. Small crystals of alkali-substituted KNB (Cs0.3K0.7NB) and RNB (Na0.07Rb0.93NB and K0.44Rb0.56NB) were also grown by spontaneous nucleation to provide additional information on the structure-property relationships of the XYB2O6 compounds. Single crystals of both KNB and RNB measuring similar to 20 x 10 x 10 mm(3) were grown by top-seeded solution growth (TSSG) using the same melt compositions as used in spontaneous nucleation. These crystals contained large densities of bubbles and solvent inclusions. However, small (5 x 5 x 3 mm(3)) defect-free samples could be cleaved from these crystals. Even larger single crystals ( similar to 38 x 33 x 6 cm(3)) of RNB were grown by TSSG from an Rb2MoO4 flux and these were free of inclusions. The potential of these single crystals for application in nonlinear optical devices was assessed by X-ray diffraction, optical absorption, laser damage threshold and efficiency of second harmonic generation at 532 nm.