Disclosed are processes for oligomerizing ethylene by contacting a catalyst system, ethylene, and optionally hydrogen to form an oligomer product in a reaction zone, wherein the catalyst system comprises: a chromium component comprising an N2-phosphinyl amidine chromium compound complex, an N2-phosphinyl formamidine chromium compound complex, and/or an N2-phosphinyl guanidine chromium compound complex, and an aluminoxane; wherein the aluminoxane is characterized by 400 MHz proton NMR in which: (a) the ratio of peaks found in the range of −0.86 ppm to −0.74 ppm to peaks found in a range of −0.03 ppm to 0.07 ppm is less than or equal to 2.8:1; (b) the ratio of peaks found in the range of −0.03 ppm to 0.025 ppm to peaks found in a range of 0.025 ppm to 0.07 ppm is less than or equal to 15:1; and/or (c) the ratio of peaks found in a range of −0.86 ppm to −0.78 ppm to peaks found in the range of −0.78 ppm to −0.74 ppm is less than or equal to 6.5:1.