A new type of calculi is proposed for a first order linear temporal logic. Instead of induction-type postulates the introduced calculi contain a similarity saturation principle, indicating some form of regularity in the derivations of the logic. In a finitary case we obtained the finite set of saturated sequents, showing that “nothing new” can be obtained continuing the derivation process. Instead of the ω-type rule of inference, an infinitary saturated calculus has an infinite set of saturated sequents, showing that only a “similar” sequents can be obtained continuing the dérivation process. The saturation calculi have some resemblance with resolution-like calculi.