We numerically investigate the anomalous interaction dynamics of nonparaxial accelerating beams in nonlocal nonlinear media. We find that stationary breathing bound states of spatial solitons can be formed with the help of nonlocality in the in-phase case. But it would be difficult to generate the bound states when the input amplitudes between the separated beams are different. Interestingly, the spatial solitons formed in the interactions with different amplitudes can propagate along the sinusoidal path, and the path can be modulated flexibly by altering the degree of nonlocality. Furthermore, it is found that the nonoverlapping bound states can be generated from anomalous interactions in the out-of-phase case. In addition, the parameter of longitudinal vortex of order can have different impacts on the interaction dynamics of the in-phase case and out-of-phase case, respectively. Especially, it is noted that the paraxial limit is taken on all the simulation results for simplicity.