With the advent of new spectroscopic surveys from ground and space, observing up to hundreds of millions of galaxies, spectra classification will become overwhelming for standard analysis techniques. To prepare for this challenge, we introduce a family of deep learning tools to classify features in one-dimensional spectra. As the first application of these Galaxy Spectra neural Networks (GaSNets), we focus on tools specialized in identifying emission lines from strongly lensed star-forming galaxies in the eBOSS spectra. We first discuss the training and testing of these networks and define a threshold probability, PL, of 95% for the high-quality event detection. Then, using a previous set of spectroscopically selected strong lenses from eBOSS, confirmed with the Hubble Space Telescope (HST), we estimate a completeness of ~80% as the fraction of lenses recovered above the adopted PL. We finally apply the GaSNets to ~1.3M eBOSS spectra to collect the first list of ~430 new high-quality candidates identified with deep learning from spectroscopy and visually graded as highly probable real events. A preliminary check against ground-based observations tentatively shows that this sample has a confirmation rate of 38%, in line with previous samples selected with standard (no deep learning) classification tools and confirmed by the HST. This first test shows that machine learning can be efficiently extended to feature recognition in the wavelength space, which will be crucial for future surveys like 4MOST, DESI, Euclid, and the China Space Station Telescope.