  We report a newly found two-stage mechanism of electron acceleration near
X-lines of 3D collisionless guide-field magnetic reconnection in the
non-relativistic regime typical, e.g., for stellar coronae. We found that after
electrons are first pre-accelerated during the linear growth of reconnection,
they become additionally accelerated in the course of the nonlinear stage of 3D
guide-field magnetic reconnection. This additional acceleration is due to the
filamentation of electric and magnetic fields caused by streaming
instabilities. In addition to enhanced parallel electric fields, the
filamentation leads to additional curvature-driven electron acceleration in the
guide-field direction. As a result, part of the the accelerated electron
spectra becomes a power law with a spectral index of $\sim-1.6$ near the
X-line. This second stage of acceleration due to nonlinear reconnection is
relevant for the production of energetic electrons in, e.g., thin current
sheets of stellar coronae.
