Eighteen structures of new organic alkalides (M+@n(6)adz)M'(-) (M, M' = Li, Na, K; n = 2, 3) with the alkalimetal cation M' lying near the center of the adz cage and the alkali-metal anion M'(-) located outside are obtained with all real frequencies. They exhibit very large static first hyperpolarizabilities (beta(0)) up to 3.2 x 105 an, which exceeds the record value of beta(0) = 1.7 x 10(5) an for nonlinear optical compounds [Chem.-Eur. J. 1997, 3, 1091]. All potassides (M+@n(6)adz)K-(M = Li, Na, K; n = 2, 3) have considerably large beta(0) values (1.6 x 10(5)-3.2 x 10(5) au) much larger than the beta(0) value (3.6 x 10(4) au) of the previously designed cuplike alkalide Li+(calix[4]pyrrole)K-[J. Am. Chem. Soc. 2006, 128, 1072]. This shows that the 2(6)adz and 3(6)adz cage complexants are preferable to cuplike calix[4]pyrrole complexant in enhancing the first hyperpolarizability. The effect of cage size of the complexant on the first hyperpolarizability is also presented here: in most cases, the smaller cage complexant corresponds to the larger beta(0) value. Moreover, the crucial role by the alkali-metal anion in the large first hyperpolarizability of these alkalides is revealed. These results may provide new means for designing high-performance nonlinear optical materials.