  In this work we obtain algebraicity results on special $L$-values attached to
Siegel-Jacobi modular forms. Our method relies on a generalization of the
doubling method to the Jacobi group obtained in our previous work, and on
introducing a notion of near holomorphy for Siegel-Jacobi modular forms. Some
of our results involve also holomorphic projection, which we obtain by using
Siegel-Jacobi Poincar\'e series of exponential type.
