The super-Liouville equation on the half-line

A recursive formula for an infinity of integrals of motion for the super-Liouville theory is derived. The integrable boundary interactions for this theory and the super-Toda theory based on the affine superalgebra B(1) (0, 1) are computed. In the first case the boundary interactions are unambiguously determined by supersymmetry, whilst in the latter case there are free parameters.