  We present a detailed study of the analytic structure, BPS spectra and
superconformal points of the $ N=2 $ susy $ SU(2) $ gauge theories with $
N_f=1,2,3 $ massive quark hypermultiplets. We compute the curves of marginal
stability with the help of the explicit solutions for the low energy effective
actions in terms of standard elliptic functions. We show that only a few of
these curves are relevant. As a generic example, the case of $ N_f=2 $ with two
equal bare masses is studied in depth. We determine the precise existence
domains for each BPS state, and show how they are compatible with the RG flows.
At the superconformal point, where two singularities coincide, we prove that
(for $ N_f=2 $) the massless spectrum consists of four distinct BPS states and
is S-invariant. This is due to the monodromy around the superconformal point
being S, providing strong evidence for exact S-duality of the SCFT. For all $
N_f $, we compute the slopes $ \omega $ of the $ \beta $-functions at the fixed
point couplings and show that they are related to the anomalous dimensions $
\alpha $ of $ u= < tr \phi^2 > $ by $ \omega= 2 (\alpha -1) $.
