We study the properties of unstable nuclei including the possibility o
f triaxial deformation in the relativistic mean-field theory. We calcu
late the energy surfaces of various light mass nuclei: O-16, Ca-40, Ne
-20, Ne-24 and Mg-24 and a series of even mass sulfur isotopes, in the
beta gamma plane. We find the well-known spherical solution for the O
-16 and Ca-40 nuclei and strong prolate solutions for Ne-20, Ne-24 and
Mg-24, which are in agreement with the experimental data and the non-
relativistic density-dependent Hartree-Fock results. For the sulfur is
otopes, we find that the energy minimum moves from a prolate shape bel
ow S-46 through triaxial shapes for S-48-52 to an oblate shape above S
-54.