Usually we distinguish between "transient" and "steady-state" behaviour. This can apply to AC and DC systems.
Consider a capacitor in a series RC circuit (in DC). When we switch on the power, there is some elapsed time while the capacitor charges up. That initial period is described by the "transient" behaviour. When the capacitor is fully charged, it is said to be in steady-state (in this case acting like an open circuit).
The equation for the capacitor voltage in transient behaviour is
V(t) = Vs - exp(-t/RC)
Now if you let t approach infinity, the exponential term goes to zero, and V(t) = Vs, which is independent of time. This shows two concepts: Steady-state behavoiur is time-invariant (it does not matter if t=10 or t=100000000), and that transient behaviour is a "general" case of a circuit.
An AC system can also be said to have transient and steady-state behaviour, although the difference is a bit more subtle. Conceptually, you could do the same analysis as above with RMS values, and you'll see that in AC "steady-state" the RMS values are constant, and during transient behaviour, the RMS values change with time.
We tend to learn about steady-state because the analysis is much simpler, but a more accurate model of a circuit (derived from its differential equation) will give the transient (aka "with time") behaviour.
In practical terms, it is important to consider transients because this is usually where things blow up. A circuit that has been running happily for 6 hours probably won't explode. A filament light bulb, for example, conducts significantly higher current when it is cold (i.e. right when you turn it on), which is why lights seldom burn out while they're on. But when you hit the switch and hear a *pop*, that is the transient behaviour of the current destroying the filament.