  The paper is devoted to the study of the orientability of the moduli spaces
of real pseudoholomorphic curves in real symplectic manifolds. We begin by
extending the results we obtained in \cite{article1}. Namely, we consider a
complex vector bundle $(N,c_N)$ equipped with a real structure over a real
curve $(\Sigma_g,c_{\Sigma})$ of genus $g \in \NN$, and we give a description
of the action of an automorphism of $(N,c_N)$ on the orientations of the
determinant bundle over the space of all Cauchy-Riemann operators on $(N,c_N)$.
In the second part, we use the previous decription to compute the first
Stiefel-Whitney class of the moduli space of real pseudoholomorphic curves in
many cases. We show for example that the real pseudoholomorphic curves with
non-empty real part in the complex projective space of dimension three form an
orientable moduli space for a generic almost complex structure.
