The spectroscopic constants (SCs) of the ground states and the first excited states of gallium monohalide diatomic molecules are carried out, by using the density functional theory (DFT) with different local density approximation (LDA) and general gradient approximations (GGA), for the first time. The results obtained by different LDAs and GGAs are compared with the observed values and the theoretical results; and also compared to the results calculated with and without a combined scalar and zero order regular approximation (ZORA) relativistic corrections, respectively, showing that DFT with appropriate LDAs and GGAs are fairly successful for dealing with the ground and first excited states of these molecules with heavy elements. Furthermore, the scalar and ZORA relativistic correction are suggested as good approximate approaches. (C) 2002 Elsevier Science B.V. All rights reserved.