This research was carried out with the aim to evaluate the anaerobic digestion (AD) of llama and dromedary dungs (both untreated and trampled) in batch mode at mesophilic temperature (35 °C). The biochemical methane potential (BMP) tests with an inoculum to substrate ratio of 2:1 (as volatile solids (VS)) were carried out. The methane yield from trampled llama dung (333.0 mL CH4 g−1 VSadded) was considerably higher than for raw llama, raw and trampled dromedary dungs (185.9, 228.4, 222.9 mL CH4 g−1 VSadded, respectively). Therefore, trampled llama dung was found to be the best substrate for methane production due to its high content of volatile solids as well as its high nitrogen content (2.1%) and more appropriate C/N ratio (23.6) for AD. The experimental data was found to be in accordance with both first-order kinetic and transference function mathematical models, when evaluating the experimental methane production against time. By applying the first-order kinetic model, the hydrolysis rate constants, kh, were found to be 19% and 11% higher for trampled dungs in comparison with the raw dung of dromedary and llama, respectively. In addition, the maximum methane production rate (Rm) derived from the transference function model for trampled llama dung (22.0 mL CH4 g−1 VS d−1) was 83.3%, 24.4% and 22.9% higher than those obtained for raw llama manure and for raw and trampled dromedary dungs, respectively.