Magnetotransport measurements have been performed on two-dimensional electron gases formed at InAs(110) surfaces covered with a submonolayer of Fe. Hysteresis in the magnetoresistance, a difference in remanent magnetoresistance between zero-field-cooling procedures and field-cooling procedures, and logarithmic time-dependent relaxation after magnetic field sweep are clearly observed at 1.7 K for a coverage of 0.42 monolayer. These features are associated with spin-glass ordering in the Fe film.PACS numbers: 75.70. Ak, 73.25.+i, 75.50.Lk Spin glasses are magnetic systems with randomly competing interactions. They have attracted great interest during the last few decades [1,2,3]. Spin-glass models and related methods have also been useful in other areas of science such as simulation of protein folding [4] and optimization problems in computer science [5]. Most of the attempts to understand spin glasses have been concerned with the behavior in three dimensions. It is generally believed that, in two dimensions, the spin-glass ordering does not occur at nonzero temperature. The lower critical dimension of spin-glass ordering has been shown to be d l > 2 for Heisenberg spins [6] and XY spins [7], and Ising spins with Gaussian distribution of disorder [8,9]. Although the situation for the Ising model with bimodal (±J) disorder was controversial [10,11], recent theoretical investigations do not support the existence of the spin-glass phase for T > 0 [12,13,14]. On the other hand, numerical calculations have demonstrated that the spin-glass-like ordering temperature can be nonzero for a two-dimensional (2D) Ising model with random nearestneighbor interactions and ferromagnetic second-neighbor interactions [15,16]. Experimentally, spin-glass behavior was found in thin films [17,18,19,20] and layered compounds [21,22,23]. However, no observation has been reported for a single layer system with strict two dimensionality.Submonolayer films of magnetic materials adsorbed on nonmagnetic substrates are promising candidates for 2D spin-glass systems. A random distribution of adsorbates can be obtained by deposition at low substrate temperatures, where surface diffusion is minimal and island growth is limited. In the case that the sign of the interaction depends on the relative position of adatoms, a competition between ferromagnetic and antiferromagnetic interactions is expected. As the substrate, narrow band-gap III-V semiconductors have a remarkable property. It is well known that a two-dimensional electron gas (2DEG) can be easily formed on the surface of InAs and InSb. Photoelectron spectroscopy measurements have shown that the position of the Fermi level lies above the conduction-band minimum at cleaved (110) surfaces with various kinds of adsorbed materials [24,25]. Recently the present authors have performed magnetotransport measurements on inversion layers formed on cleaved surfaces of p-type InAs [26,27] and InSb [28] covered with submonolayers of Ag or alkali metals. The observed coverage dependence of the Hall mobi...