Measurements of commensurability oscillations in GaAs/AlGaAs two-dimensional (2D) hole systems grown on GaAs (311)A substrates reveal a remarkable anisotropy: the amplitude of the measured commensurability oscillations along the [233] direction is about 100 times larger than along [011]. For 2D electron systems at similar interfaces, however, we observe nearly isotropic oscillations, suggesting that the anomalous anisotropy is intrinsic to GaAs 2D holes at the (311)A interface. GaAs/AlGaAs heterojunctions and quantum wells, grown on GaAs (311)A substrates and modulation-doped with Si, are of considerable current interest. These structures can contain very high mobility two-dimensional hole systems (2DHSs), and have already shown a number of novel phenomena including signatures of magnetic-fieldinduced Wigner crystallization [1] and metal-insulator transition at zero magnetic field [2][3][4][5]. These systems are also known to exhibit an in-plane transport anisotropy [6][7][8]; the mobility along the [233] direction is typically larger than along [011] by a factor of 2 to 5. Here we report the observation of commensurability oscillations (COs) revealing a surprisingly large anisotropy in the amplitude of the COs measured along these two directions in this system. We recall that COs refer to the oscillations in the magnetoresistance of a 2D carrier system whose density has a lateral periodic modulation [9,10]. In a simple, semiclassical model [11], the oscillations can be related to the classical cyclotron orbit diameter of the carriers becoming commensurate with a multiple integer of the period a of the potential. The anisotropy of the COs we observe in the 2DHSs is too large to be explained by a simple argument based on mobility anisotropy.Our samples were grown by molecular-beam epitaxy (MBE) on GaAs (311)A substrates, and have lowtemperature mobility in the range of 1.7×105 cm 2 /V s to 1.6×106 cm 2 /V s. The sample structure is shown schematically in Fig. 1. Arrays of 1000Å-thick PMMA strips were defined perpendicular to the two arms of an L-shaped Hall bar pattern which was made by electronbeam lithography and 5000Å-deep wet etching. The two arms of the Hall bar were aligned along the [233] and [011] directions. The periods of PMMA strips range from 2000Å to 3000Å and their widths equal half of their periods. A front gate was made by evaporating 50Å of Ti and 2000Å of Au. We measured the longitudinal magnetoresistance as a function of perpendicular magnetic field B, at T ≈ 0.5K using a standard low-frequency lock-in technique.We studied 2DHSs confined in both triangular and square quantum wells. The low-B magnetoresistances measured along the [233] and [011] directions are represented by R [233] and R [011] , respectively. Both R [233] and R [011] are measured with the current running perpendicular to the direction of the PMMA strips (see Fig. 1). We find an enormous amplitude anisotropy in the COs measured along the [233] and [011] directions. In the triangular well sample, as shown in Fig. 2, we ob...