A local minimum is found in the O-g(+) long range potential curves of the K-2 and Rb-2 alkali dimers. This well-of magnitude 42 cm(-1) for K-2 and 93 cm(-1) for Rb-2-is located above the first ns +n(2)P(3/2) dissociation limit and metastable states could be populated using laser light blue detuned compared to the resonance line. To compute the previously unknown energies and Lifetimes of these quasibound states, two grid methods are employed. One method is based on diagonalizing a Fourier grid Hamiltonian, the other uses a propagation technique in imaginary time to filter out vibrational eigenfunctions. Equivalent results are given by both methods. Then the Lifetimes are extracted from the correlation function obtained by propagation in real time of these numerical vibrational wave functions, The methods are employed both in adiabatic representation with one electronic potential curve and in diabatic representation with two potential curves. Two quasibound states are found for K-2, and three for Rb-2 above seven stable bound states. Their lifetimes vary from 20 ps to 3 ns. (C) 1997 American Institute of Physics.