The sorption of methylene blue (MB) and basic yellow 28 (BY28) dyes in water on Ag@ZnO/MWCNT (Ag‐doped ZnO loaded on multiwall carbon nanotubes) nanocomposite is investigated in a batch process, optimizing starting initial dye concentration, sonication time and adsorbent mass. Isotherms and kinetic behaviours of MB and BY28 adsorption onto Ag@ZnO/MWCNT were explained by extended Freundlich and pseudo‐second‐order kinetic models. Ag@ZnO/MWCNT was synthesized and characterized using X‐ray diffraction, energy‐dispersive X‐ray spectroscopy, field emission scanning electron microscopy and Brunauer–Emmett–Teller analysis. According to the experimental data, adaptive neuro‐fuzzy inference system (ANFIS), generalized regression neural network (GRNN), backpropagation neural network (BPNN), radial basic function neural network (RBFNN) and response surface methodology (RSM) were developed, and applied to forecast the removal performance of the sorbent. The influence of process variables (i.e. sonication time, initial dye concentration, adsorbent mass) on the removal of MB and BY28 was considered by central composite rotatable design of RSM, GRNN, ANFIS, BPNN and RBFNN. The performances of the developed ANFIS, GRNN, BPNN and RBFNN models were compared with RSM mathematical models in terms of the root mean square error, coefficient of determination, absolute average deviation and mean absolute error. The coefficients of determination calculated from the validation data for ANFIS, GRNN, BPNN, RBFNN and RSM models were 0.9999, 0.9997, 0.9883, 0.9898 and 0.9608 for MB and 0.9997, 0.9990, 0.9859, 0.9895 and 0.9593 for BY28 dye, respectively. The ANFIS model was found to be more precise compared to the other models. However, the GRNN method is much easier than the ANFIS method and needs less time for analysis. So, it has potential in chemometrics and it is feasible that the GRNN algorithm could be applied to model real systems. The monolayer adsorption capacity of MB and BY28 was 292.20 and 287.02 mg g−1, respectively.