Linear and nonlinear dielectric studies of AgNb(1-x)Ta(x)O(3) (ATN) ceramics (x ≤ 0.6) were carried out in the temperature range of 80 to 673K. The temperature dependences of third-order nonlinear electric susceptibility X3'(T) exhibit two distinct maxima: at the temperature of the weak ferroelectric phase appearance, M(1)-M(2) transition, and at the temperature of the Nb/Ta ion dynamics freezing, Tf. For AgNbO3, they appear at 325K and 448K, respectively. With increasing Ta concentration, both maxima shift toward lower temperature: 4K/%Ta (M(1)-M(2)) and 5.6K/%Ta (T(f)). The X3' (T) maxima indicate changes of the Nb/Ta ion dynamics and their contribution to electric susceptibility. At T(f), a partial freezing of the Nb/Ta ion displacements to the disordered antipolar, antiferroelectric array takes place. At the M(1)-M(2) transition, further freezing of Nb/Ta displacements to polar weak relaxor ferroelectric or dipolar glass transition occurs. This polar state coexists with the ground antiferroelectric state. Studies of the aging process showed that below T(f) the aging influence on electric susceptibility is substantial, whereas above Tf it may be neglected. This means that for ATN ceramics in the concentration range used for applications, there is no aging process in the room temperature region, which is an additional advantage of this system.