The author tries to outline Fregeś semantics for indexical expressions. The task is rather problematic because there seems to be some inconsistency between general principles of Fregeś semantics and requirements posed by him for semantics of indexicals. The main problem arises when we ask which kind of sense ought to be expressed by an indexical expression. Two proposals as possible answers are discussed, one suggested by John Perry, the other by Pavel Tichý. Both proposals are in part right but there are some arguments against their general validity. Then the author sketches another suggestion which preserves the main contributions of the above proposals but nullifies their mistakes.