The white LED lights tend to run directly from the batteries with no current limiting resistors, especially the cheapies.

This makes them very bright with fresh batteries, but that doesn't last long before they dim a bit as the more stable battery voltage kicks in. This is especially true for HiMH or NiCDs. The LED will remain at a stable brightness for a long time as the battery remains in this phase. Then, as the battery gets to the empty point, the voltage drops and this reduces the LED current rapidly, this is a sort of negative feedback so the LEDS keep glowing dimly for ages and ages. Not very useful for seeing where you're going, but light nevertheless.

Eg, I have a 3W Luxeon flashlight that I use for night commuting, running off 3 AAA cells. The light is very bright for a few minutes, then tapers off to being nice and bright, quite adequate for seeing where I'm going, then after say 2h it gradually dims and will keep going like that for another 24h.

With incandescents, the current demand actually goes up as it dims so there is a sudden loss of light when the batteries go flat.