A series of alkyl-grafted copolymers based on styrene-maleic anhydride (SMA) copolymers were synthesized by esterification of SMA with several long chain normal aliphatic alcohols. The prepared copolymers were characterized by FT-IR and 1H NMR and DSC. The dielectric behavior of these copolymers was investigated in the frequency 20–105 Hz and temperature −40 to 180 °C ranges. Two relaxation processes were observed, α, and β-relaxation. The former is associated with the glass-rubber transition and is characterized by the Vogel–Fulcher–Tammann temperature dependence and the latter relaxation is related to the local motion of the ester side groups attached to the polymer backbone. The apparent activation energy for the β-relaxation was found to depend significantly on the alkyl chain length. The dielectric analysis of the β-relaxation process detected is discussed.