Active galactic nuclei (AGNs) in low surface brightness galaxies (LSBGs) have received little attention in previous studies. We present a detailed spectral analysis of 194 LSBGs from the Impey et al. (1996, Cat. J/ApJS/105/209) APM LSBG sample which has been observed spectroscopically by the Sloan Digital Sky Survey Data Release 5 (SDSS DR5). Our elaborate spectral analysis enables us to carry out, for the first time, reliable spectral classification of nuclear processes in LSBGs based on the standard emission line diagnostic diagrams in a rigorous way. Star-forming galaxies are common, as found in about 52% of LSBGs.We find that, contrary to some previous claims, the fraction of galaxies that contain AGNs is significantly lower than that found in nearby normal galaxies of high surface brightness. This is qualitatively in line with the finding of Impey et al. This result holds true even within each morphological type from Sa to Sc. LSBGs that have larger central stellar velocity dispersions or larger physical sizes tend to have a higher chance of harboring an AGN. For three AGNs with broad emission lines, the black hole masses estimated from the emission lines are broadly consistent with the well known M-{sigma}* relation established for normal galaxies and AGNs.