The electrical and thermal characteristics of three ohmic contact structures: (i) in situ deposited epitaxial Al on delta -doped GaAs, (ii) evaporated Au-Ge on delta -doped GaAs (iii) evaporated Au-Ge on GaAs were compared with each other. The I-V characteristics of the non-alloyed Au-Ge and the epitaxial Al, as-deposited, on delta -doped GaAs were linear, whereas the non-alloyed Au-Ge contact on GaAs showed a nonlinear I-V characteristic, as expected. The specific contact resistivity ( rho c) of the non-alloyed Au-Ge contacts on delta -doped GaAs was 1.4*10-6 Omega cm2, whereas it was 9*10-7 Omega cm2 for the epitaxial Al contacts on delta -doped GaAs, which is the lowest ever reported for a pure metal on delta -doped GaAs. No value of the specific contact resistivity ( rho c) could be obtained for the Au-Ge contacts on GaAs because of the nonlinearity of the I-V characteristics. After an alloying process at 450 degrees C all samples showed linear I-V characteristics. The specific contact resistivity of all samples varied inversely with the n+ doping concentration up to 5*1017 cm-3. Above this concentration the specific contact resistivity of the Au-Ge and epitaxial Al contacts on delta -doped GaAs was constant and hardly changed after alloying. Our results confirm that the well known double-barrier (metal-n+-n) model is valid for the ohmic contact on delta -doped GaAs.