  The dynamic dipole polarizabilities for the Li atom and the Be+ ion in the 2s
and 2p states are calculated using the variational method with a Hylleraas
basis. The present polarizabilities represent the definitive values in the
non-relativistic limit. Corrections due to relativistic effects are also
estimated. Analytic representations of the polarizabilities for frequency
ranges encompassing the n=3 excitations are presented. The recommended
polarizabilities for ^7Li and ^9Be+ were 164.11 \pm 0.03 a.u. and 24.489 \pm
0.004 a.u..
