In this paper, we consider DS-CDMA/OFDM spectrum sharing systems and obtain the achievable capacity of the secondary service under different subchannel selection policies in the fading environment. Subchannel selection policies are divided into two categories: uniform subchannel selection, and nonuniform subchannel selection. Uniform subchannel selection is preferred for cases where a priori knowledge on subchannels state information is not available at the secondary transmitter. For cases with available a priori knowledge on subchannels state information, we study various nonuniform subchannel selection policies. In each case, we obtain the optimum secondary service power allocation and the corresponding maximum achievable capacity. Then we present results on the scaling law of the opportunistic spectrum sharing in DS-CDMA/OFDM systems with multiple users. Numerical results show that the optimal subchannel selection is based on the minimum value of the subchannel gain between the secondary transmitter and the primary receiver.