The Demo Videos are videos used as demonstrations in the main menu of the Games. They appear in TimeSplitters 1 and TimeSplitters 2, but not in Timesplitters: Future Perfect, which instead replaces the demos with a compilation of gameplay from the Story mode which features music from the Scotland The Brave tank boss. They are never in order, but follow a pattern.
Not all levels are featured as demontrations in TimeSplitters 1, the ones that are shown are (in order of appearance):
Less levels are shown in TimeSplitters 2, only half of the story levels are shown, while in TimeSplitters 1 more than two thirds are shown. The demos are (in order of appearance):