  In this paper, we characterize quasi-integrable modules, of nonzero level,
over twisted affine Lie superalgebras. We show that quasi-integrable modules
are not necessarily highest weight modules. We prove that each quasi-integrable
module is parabolically induced from a cuspidal module, over a finite
dimensional Lie superalgebra having a Cartan subalgebra whose corresponding
root system just contain real roots; in particular, the classification of
quasi-integrable modules is reduced to the known classification of cuspidal
modules over such Lie superalgebras.
