This paper presents a performance analysis of the single antenna interference cancellation (SAIC) and the multiple antenna interference cancellation (MAIC) techniques in the presence of non null frequency offsets of both the signal of interest (SOI) and interference, that are neither corrected nor compensated, in terms of signal to interference plus noise ratio (SINR) and bit error rate (BER). General theoretical expressions of the SINR and BER are given for BPSK SOI and interference. To obtain engineering insight, the particular case of the SAIC with no return to zero (NRZ) pulse shape filters is considered, where simple expressions are given and analyzed. It is proved in particular that the performance more deteriorates for non null frequency offset of the interference than for non null frequency offset of the SOI. Finally illustrative examples are presented in order to specify the validity domain of our approximations and to quantify the obtained results in the context of the global system for mobile communication (GSM) standard