  We give a complexity dichotomy for the Quantified Constraint Satisfaction
Problem QCSP(H) when H is a reflexive tournament. It is well-known that
reflexive tournaments can be split into a sequence of strongly connected
components H_1,...,H_n so that there exists an edge from every vertex of H_i to
every vertex of H_j if and only if i<j. We prove that if H has both its initial
and final strongly connected component (possibly equal) of size 1, then QCSP(H)
is in NL and otherwise QCSP(H) is NP-hard.
