A process for producing clean steel products with low nitrogen content below 35 ppm, in a steelmaking plant comprising a direct reduced iron (DRI) source, an electric arc furnace (EAF), a degassing system (DS), and a continuous casting system (CC), wherein said process comprises a first stage of melting, and refining in said electric arc furnace (EAF) a metallic iron charge comprising steel scrap and/or one or more of direct reduced iron (DRI), hot briquetted iron (HBI), pig iron, or other metallic iron-bearing materials, a second stage of tapping molten steel from the electric arc furnace (EAF) into a ladle, a third stage of exposing molten steel to a pressure below the atmospheric pressure in said degassing system (DS) and a fourth stage of casting molten steel to a steel product in said continuous casting (CC), said process being characterized by said hot metallic iron charge having a maximum of 60 ppm of sulfur and 35 ppm, preferably below 30 ppm of nitrogen, and a carbon content above 2.5%, forming a first foamy slag having a predetermined composition during said first process stage, maintaining said first foamy slag in a foamy state during said first process stage by controlling the feed of fluxes, oxygen, and carbon to said electric arc furnace (EAF), and forming a second desulfurizing slag during said second process stage, having a predetermined composition capable of continuing the desulfurization and providing thermal insulation and chemical insulation of the molten steel during the subsequent process stages.