To clarify the heavy fermion properties of Th2Zn17-type Ce2CuxAl17-x (6.75 less than or equal to x less than or equal to 8.25), we have systematically measured the electrical resistivity including the magnetoresistance, the magnetic susceptibility and the specific heat. In the electrical resistivity measurement for x = 8.0, no magnetic order was clearly observed down to 60 mK and the magnetic contribution to the specific heat, C-m/T, reached extremely large values of C-m/T = 3.0 (at 0.7 K), 2.4 (at 0.8 K) and 1.7 J/K-2 mol-Ce (at 1.4 K) for x = 8.0, 7.5 and 7.0, respectively. A T-2 dependence of the electrical resistivity was also observed below 0.4 K for x = 8.0 and below 0.6 K for x = 7.0 and 7.5, indicating that Ce2CuxAl17-x is a coherent heavy fermion system. However, the possibility of the coexistence of short-range magnetic order resulting from the random distribution of Cu and Al could not be entirely excluded. We discuss the large C-m/T Values at temperatures close to 0 K in terms of the x dependence of the Kondo temperature, T-K, and also discuss the differences between the magnetic properties of heavy fermion compounds such as CeCu6 and those of Ce2CuxAl17-x.