Intraocular lens with accommodation capacity comprising an optical power system comprising a first optical member with variable and dynamic optical power, and which comprises two surfaces (1a, 1b) respectively corresponding to an anterior surface and a posterior surface at least one of which having a curvature that is capable of becoming deformed elastically in response to traction forces of the ciliary muscle of the eye, an equatorial region about said surfaces (1a, 1b), as well as a second optical member with a fixed optical power, with a curved anterior side and a curved posterior side, the second optical member being associated to the first optical member in such a manner that the first optical member and the second member have a joint optical power determined by a combination of the fixed optical power of the second optical member and the dynamic optical power of the first optical member, an anchoring system to anchor the first optical member to at least a portion of the capsular bag of the crystalline lens, to transmit to the first optical member traction forces generated by the ciliary muscle and transmitted to the capsular bag by zonular fibers, the capsular bag comprising, in its natural state, an anterior capsule, a posterior capsule and an equatorial capsule, the anchoring system selected among mechanical fastening systems, biocompatible adhesive systems, microstructure systems fostering capsular fibrosis, and combinations thereof, the second optical member is joined to the first optical member such that at least respective central portions of one of the curved sides (2a, 2b) of the second optical member and of at least one of the surfaces (1a, 1b) of the first optical member are in contact with each other; the joint optical power is variable between a condition of minimum optical power corresponding to a condition of disaccommodation where the intraocular lens is capable of focusing the eye to a far vision distance, and a condition of accommodation where the intraocular lens is capable of focusing the eye to a reading distance; characterized in that: - the first optical member is made of a preformed deformable material and has a predetermined preform maximum curvature and maximum optical power in its accommodating position; the first optical member and the anchoring system are designed to change the curvature of at least one of the surfaces (1a,1b) of the first optical member progressively between the predetermined preform of maximum curvature corresponding to the condition of maximum accommodation in response to a minimum effective traction force of the ciliary muscle received by the anchoring system, and a minimum curvature corresponding to the condition of disaccommodation in response to a maximum effective traction force of the ciliary muscle received by the anchoring system; and in that: - the anchoring system is a discrete set of more than three anchoring points to anchor the first optical member to at least a portion of the capsular bag of the crystalline lens. an optical power system comprising a first optical member with variable and dynamic optical power, and which comprises two surfaces (1a, 1b) respectively corresponding to an anterior surface and a posterior surface at least one of which having a curvature that is capable of becoming deformed elastically in response to traction forces of the ciliary muscle of the eye, an equatorial region about said surfaces (1a, 1b), as well as a second optical member with a fixed optical power, with a curved anterior side and a curved posterior side, the second optical member being associated to the first optical member in such a manner that the first optical member and the second member have a joint optical power determined by a combination of the fixed optical power of the second optical member and the dynamic optical power of the first optical member, an anchoring system to anchor the first optical member to at least a portion of the capsular bag of the crystalline lens, to transmit to the first optical member traction forces generated by the ciliary muscle and transmitted to the capsular bag by zonular fibers, the capsular bag comprising, in its natural state, an anterior capsule, a posterior capsule and an equatorial capsule, the anchoring system selected among mechanical fastening systems, biocompatible adhesive systems, microstructure systems fostering capsular fibrosis, and combinations thereof, the second optical member is joined to the first optical member such that at least respective central portions of one of the curved sides (2a, 2b) of the second optical member and of at least one of the surfaces (1a, 1b) of the first optical member are in contact with each other; the joint optical power is variable between a condition of minimum optical power corresponding to a condition of disaccommodation where the intraocular lens is capable of focusing the eye to a far vision distance, and a condition of accommodation where the intraocular lens is capable of focusing the eye to a reading distance; - the first optical member is made of a preformed deformable material and has a predetermined preform maximum curvature and maximum optical power in its accommodating position; - the anchoring system is a discrete set of more than three anchoring points to anchor the first optical member to at least a portion of the capsular bag of the crystalline lens.