This paper investigates the performance of differential-phase Orthogonal Frequency Division Multiplexing (OFDM) over frequency-selective multipath Nakagami-m radio fading channels. A closed form for the average signal to noise/interference ratio in the presence of the selective multipath fading channel and additive white Gaussian noise (AWGN) is derived. The results reveal that the system performance is impacted by the interference between the adjacent OFDM frames in two successive signaling intervals which is called Inter-Symbol-Interference (ISI). In addition, the system will possibly be distorted when the orthogonality between the adjacent subcarriers is ceased, creating Inter-Channel-Interference (ICI). This paper also studies the bit-error-rate (BER) performance of the differential-phase OFDM system over the Nakagami-m channel in the presence of AWGN, ISI, and ICI under different conditions and parameters. Moreover, the effect of adding the guard period and the number of subchannels on the probability of error is analyzed. The IEEE 802.11a standard parameters with 64 subcarriers and a decaying exponential power delay profile with root-mean-square value of 129 ns are used in this study. The system performance is also simulated at different guard intervals, number of OFDM subcarriers, Nakagami severity parameter values, and different numbers of possible differential phases.