Crosslinked olefin polymers which are reduced in stickiness and improved in rigidity, heat resistance, light resistance, and water resistance while retaining the molding properties such as injection moldability, spinnability, film-forming properties and the physical properties such as toughness (including elongation and break strength) and tackiness; and a process for the production thereof. Crosslinked olefin polymers which are obtained by reacting an α-olefin polymer produced by polymerization of at least one α-olefin having 6 or more carbon atoms or polymerization of at least one α-olefin having 6 or more carbon atoms with at least one other α-olefin with a crosslinking agent and which satisfy the following requirements: (1) the content of units of α-olefins having 6 or more carbon atoms is 50 mol % or more, (2) the molecular weight distribution (Mw/Mn) as determined by gel permeation chromatography (GPC) is 7.0 or more in terms of polystyrene, (3) the content of components having weight-average molecular weights (Mw) of 106 or more is 5% by mass or more as determined by GPC, and (4) the stereoregularity indication M4 is 75 mol % or less; and a process for the production of the polymers.