Exact and explicit string solutions in de Sitter space-time are found. (Here, the string equations reduce to a sinh-Gordon model). A new feature without flat space-time analogy appears: starting with a single worldsheet, several (here two) strings emerge. One string is stable and the other (unstable) grows as the universe grows. Their invariant size and energy either grow as the expansion factor or tend to constant. Moreover, strings can expand (contract) for large (small) universe radius at a different rate than the universe does.