By utilizing an analytical implicit solution we are able to discuss in a unified picture the characterization of the shielding current decay in superconductors with an arbitrary concave current dependence of the effective activation energy U(J). The time scales in the transient and long-time stages of the relaxation are found. The inflexion time t F which experimentalists have paid attention to is worked out. It is shown for the first time that in the case of nonlinear U(J) dependence t F could be significantly smaller than the true transient time τ * , the time scale that governs the nonlogarithmic decay on the short-time side in relaxation measurements, which is itself sample and initial-condition dependent. Furthermore, the master relaxation curve is discussed. The relation between this master curve and the underlying U(J) dependence is elaborated.