The unusual doubly excited van der Waal's state, Mg(3 p pi 3 p pi P-3(J)).Kr[(3)Sigma(-)], has been characterized using a laser-vaporization, supersonic-jet source and R2PI (Resonance Two-Photon Ionization) spectroscopy. This state is very strongly bound (D-e,= 3966 cm(-1)) and has a short bond length (R-e = 2.45 Angstrom) compared to its singly excited analogue, Mg(3 s 3 p pi P-3(J)).Kr[(II0)-I-3-], for which D-e = 267 cm(-1) and R-e = 3.48 Angstrom. In fact, this state is even more than twice as strongly bound as the ground-state Mg(3s)(+).Kr ion, where D-e = 1949 cm(-1) and R-e approximate to 2.8 Angstrom. Possible reasons for the strong van der Waal's bonding are discussed, and it is concluded that the lack of sigma-sigma repulsion because there is no Mg(3s sigma) valence electron must be a major factor; the similar ionic van der Waal's state Mg+ (3p pi).Kr[(II)-I-2], which would be obtained by removing one of the Mg(3p pi) electrons, is even more strongly bound, with D-e approximate to 7200 cm(-1) [J. S. Pilgrim, C. S. Yeh, K. R. Berry, and M. A. Duncan, J. Chem. Phys. 100, 7945 (1994)]