Single crystals of quaternary compounds in the solid solution (NaxRE1-x)AlB14 (RE=Li, Mg, rare earths (Tb, Dy, Ho, Er, Tm, Yb, Lu)) were grown by the Na-RE-Al-B system using a molten Al-self flux under an Ar gas. The single crystals of LiAlB14, NaAlB14, MgAlB14 and (NaxMg1-x)AlB14 (0.21≤x≤0) were grown; the quaternary boride (NaxLi1-x)AlB14 and (NaxRE1-x)AlB14 (Tb, Dy, Ho, Er, Tm, Yb, Lu) phases were not obtained at the single crystal growth experiment in the Na-Li-Al-B and Na-RE-Al-B systems. The as-growth LiAlB14, NaAlB14, MgAlB14, (Na0.08Mg0.92)AlB14 and (Na0.21Mg0.79)AlB14 single crystals were subjected to chemical analyses and measurements of unit-cell parameter. The homogeneity range for the solid solutions of (NaxMg1-x)AlB14 (0.21≤x≤0) crystals was studied by XRD and chemical analyses. Measurements of microhardness in air and magnetic susceptibility of crystalline samples of as-grown (NaxMg1-x)AlB14 (x=1, 0.21≤x≤0) have been measured in the temperature range of 300 K to 2 K.