A resist composition for liquid immersion lithography process, which comprises: (A) a polymer comprising (a1) alkali-soluble constitutional units each comprising an alicyclic group having both (i) a fluorine atom or a fluoroalkyl group and (ii) an alcoholic hydroxyl group, wherein the polymer changes in alkali-solubility due to the action of acid; and (B) an acid generator which generates acid due to exposure to light, and a method for forming a resist pattern using the resist composition. By the resist composition or the method, an adverse effect of the immersion liquid can be avoided while achieving high resolution and high depth of focus.