A process for producing an olefin oligomer, which comprises the steps of (1) contacting a transition metal compound with a compound represented by the formula, R.sup.1R.sup.2A--G--AR.sup.3R.sup.4, to produce a contact product (i), (2) contacting an alumoxane compound with an organoaluminum compound to produce a contact product (ii), and (3) contacting the contact product (i), the contact product (ii), and an olefin with one another, wherein A is a nitrogen atom, a phosphorus atom, an arsenic atom or an antimony atom; G is a divalent group; and R.sup.1, R.sup.2, R.sup.3 and R.sup.4 are independently of one another a hydrocarbyl group, a halogenated hydrocarbyl group, an oxygen-containing hydrocarbyl group, a sulfur-containing hydrocarbyl group, a selenium-containing hydrocarbyl group, or a tellurium-containing hydrocarbyl group.