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The paper is devoted to the study of the orientability of the moduli spacesof real pseudoholomorphic curves in real symplectic manifolds. We begin byextending the results we obtained in \cite{article1}. Namely, we consider acomplex vector bundle $(N,c_N)$ equipped with a real structure over a realcurve $(\Sigma_g,c_{\Sigma})$ of genus $g \in \NN$, and we give a descriptionof the action of an automorphism of $(N,c_N)$ on the orientations of thedeterminant 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 firstStiefel-Whitney class of the moduli space of real pseudoholomorphic curves inmany cases. We show for example that the real pseudoholomorphic curves withnon-empty real part in the complex projective space of dimension three form anorientable moduli space for a generic almost complex structure.

D\'eterminant des op\'erateurs de Cauchy-Riemann r\'eels et application \`a l'orientabilit\'e d'espaces de modules de courbes r\'eelles