In the present study, ethylene/vinyl alcohol (EVAL) copolymers with different hydroxyl contents were melt mixed with styrene/maleic anhydride (SMA) copolymers. These two copolymers have functional groups capable of reacting intermolecularly, giving stable products. All EVAL copolymers were prepared from the same ethylene/vinyl acetate (EVA) copolymer by controlled hydrolysis. The blends, prepared at constant temperature and rotation speed in the rheomixer, were characterized by Fourier transform infrared spectroscopy, differential scanning calorimetry, and thermogravimetric analysis, as well as mechanical properties and extraction experiments. All the above measurements lead to the conclusion that a certain part of hydroxyls of EVAL have reacted with anhydride groups of SMA, leading to the formation of branched and crosslinked products. The effect of (1) the molar ratio of hydroxyl/maleic anhydride functional groups, (2) the overall concentration of the functional groups, and (3) the mixing time on the structure and properties of the blends are discussed. Emphasis is given on the influence of these factors on the tensile strength, the elongation at break, and impact strength of the products.