A novel double crosslinking type transition metal compound is herein disclosed which is represented by the general formula (I) wherein M is a metallic element in the groups 3 to 10 or a lanthanoide series of the periodic table; E1 and E2 are each a cyclopentadienyl group, an indenyl group or the like, and they form a crosslinking structure via A1 and A2; A1 and A2 are each a crosslinking group comprising a hydrocarbon group of one or more carbon atoms; X is a &sgr;-bonding ligand; and Y is a Lewis base. Also disclosed are a double crosslinking type biscyclopentadienyl derivative and bisindenyl derivative for use in the above-mentioned transition metal compound, its preparation process, a catalyst for olefin polymerization using the transition metal compound, and a preparation process of an olefin polymer by the use of this catalyst.