  The propagators of the Dirac fermions are studied in the configuration
representation on the expanding portion of the $(1+3)$-dimensional de Sitter
spacetime considering a fixed vacuum of Bunch-Davies type. In this
representation the method of Koksma and Prokopec [J. F. Koksma and T. Prokopec,
Class. Quant. Grav. {\bf 26}, 125003 (2009)] is applied recovering thus the
form of the propagators in the massive case but obtaining a new result for the
left-handed massless fermions (neutrinos).
