Non-alcoholic fatty liver disease (NAFLD) is emerging as one of the most common chronic liver diseases worldwide, affecting 25% of the world population. In recent years, there has been increasing evidence for the involvement of microRNAs in the epigenetic regulation of genes taking part in the development of steatosis and steatohepatitis—two main stages of NAFLD pathogenesis. In the present study, miRNA profiles were studied in groups of patients with steatosis and steatohepatitis to compare the characteristics of RNA-dependent epigenetic regulation of the stages of NAFLD development. According to the results of miRNA screening, 23 miRNAs were differentially expressed serum in a group of patients with steatohepatitis and 2 in a group of patients with steatosis. MiR-195-5p and miR-16-5p are common differentially expressed miRNAs for both steatosis and steatohepatitis. We analyzed the obtained results: the search for target genes for the differentially expressed miRNAs in our study and the subsequent gene set enrichment analysis performed on KEGG and REACTOME databases revealed which metabolic pathways undergo changes in RNA-dependent epigenetic regulation in steatosis and steatohepatitis. New findings within the framework of this study are the dysregulation of neurohumoral pathways in the pathogenesis of NAFLD as an object of changes in RNA-dependent epigenetic regulation. The miRNAs differentially expressed in our study were found to target 7% of genes in the classic pathogenesis of NAFLD in the group of patients with steatosis and 50% in the group of patients with steatohepatitis. The effects of these microRNAs on genes for the pathogenesis of NAFLD were analyzed in detail. MiR-374a-5p, miR-1-3p and miR-23a-3p do not target genes directly involved in the pathogenesis of NAFLD. The differentially expressed miRNAs found in this study target genes largely responsible for mitochondrial function. The role of miR-423-5p, miR-143-5p and miR-200c-3 in regulating apoptotic processes in the liver and hepatocarcinogenesis is of interest for future experimental studies. These miR-374a, miR-143, miR-1, miR-23a, and miR-423 have potential for steatohepatitis diagnosis and are poorly studied in the context of NAFLD. Thus, this work opens up prospects for further studies of microRNAs as diagnostic and therapeutic biomarkers for NAFLD.