  In this paper we study polynomials $(P_n)$ which are hermitian orthogonal on
two arcs of the unit circle with respect to weight functions which have square
root singularities at the end points of the arcs, an arbitrary nonvanishing
trigonometric polynomial $\mathcal{A}$ in the denominator and possible point
measures at the zeros of $\mathcal{A}$. First we give an explicit
representation of the orthogonal polynomials $P_n$ in terms of elliptic
functions. With the help of this representation for sufficiently large $n$ the
number of zeros of $P_n$ which are in an $\epsilon$-neighbourhood of each of
the arcs are determined. Finally it is shown that the accumulation points of
the zeros of $(P_n)$ which are not attracted to the support lie on a Jordan arc
running within the unit disk from one of the arcs to the other one. The
accumulation points lie dense on the Jordan arc if the harmonic measures of the
arcs are irrational. If the harmonic measures are rational then there is only a
finite set of accumulation points on the Jordan arc.
