Single crystals of A$_{1-x}$K$_x$Fe$_2$As$_2$ (A=Ba, Sr) with high quality have been grown successfully by FeAs self-flux method. The samples have sizes up to 4 mm with flat and shiny surfaces. The X-ray diffraction patterns suggest that they have high crystalline quality and c-axis orientation. The non-superconducting crystals show a spin-density-wave (SDW) instability at about 173 K and 135 K for Sr-based and Ba-based compound, respectively. After doping K as the hole dopant into the BaFe$_2$As$_2$ system, the SDW transition is smeared, and superconducting samples with the compound of Ba$_{1-x}$K$_x$Fe$_2$As$_2$ (0 $< x leqslant$ 0.4) are obtained. The superconductors characterized by AC susceptibility and resistivity measurements exhibit very sharp superconducting transition at about 36 K, 32 K, 27 K and 23 K for x= 0.40,0.28,0.25 and 0.23, respectively.
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