In this paper, the author generalizes some results obtained by M. Epstein and the reviewer on second-order nonholonomic parallelisms, to arbitrary principal bundles. A generalized parallelism on a principal bundle \(P\to M\) is defined as a section \(M\to W^1P\) of the first prolongation \(W^1P\) of \(P\). Next, their properties are characterized in terms of induced connections. The results of M. Epstein and the reviewer were motivated by the applications to Cosserat media. It should be noted that the present results by the author are just the ones needed in the geometric characterization of the homogeneity of media with microstructure [see M. de León, “A geometrical description of media with microstructure: uniformity and homogeneity”, in: Geometry, Continua and Microstructure, Paris, May 28-29, 1997, G. A. Maugin (ed.), Travaux en Cours, Hermann, Paris, pp. 11-20 (1999)].