Single crystals of incommensurate-type superconducting cuprate phases, (M2Cu2O3)(m)(CuO2)(n) (M = Ca, Sr, Bi, Y,...), were grown. The structural features and physical properties of the crystals were correlated with the growth conditions. Superconductivity (T-c = 80 K) was observed only in the samples grown at temperatures below 960 degrees C. In the crystals obtained at higher temperatures, the superconductivity at ambient pressures was not observed. The general problem of the growth of superconducting ladder-type crystals is discussed.