In this paper, a novel categorization system of anaerobic reactors is created to frame novel upflow anaerobic filter (UAF) reactor separated into two stages (UAF-2SS) and three separated stages (UAF-3SS). Three models for the performance of UAF-2SS and UAF-3SS reactors are proposed: (1) Modified model of the Monod's Equation for estimating the substrate utilization rate (SUR) whose kinetic coefficient explains intracellular processes, (2) Model for biochemical transformation of substrate based on the Monod's Equation and the Velz's Law where the kinetic coefficient is associated to extra and intracellular processes and (3) Coupled model for transport and biochemical transformation processes integrated by two components depending on extracellular processes (adsorption and hydrolysis) and intracellular processes (fermentation/anaerobic oxidation, acidogenesis and methanogenesis). The highest degree of explanation of the proposed kinetic models for performance of UAF-2SS and UAF-3SS in the substrate removal is achieved through the coupled model.