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This paper analyzes the performance of indoor orthogonal frequency division multiplexing (OFDM) optical wireless communication systems in the presence of light emitting diode (LED) nonlinear distortions. There are several forms of optical OFDM using intensity modulation [7th Int. Symp. on Communication Systems Networks and Digital Signal Processing (CSNDSP), 2010, pp. 566-570]. In this paper, DC-biased optical OFDM (DCO-OFDM) and asymmetrically clipped optical OFDM (ACO-OFDM) are considered. ACO-OFDM produces a half-wave symmetry time signal at the output of the OFDM modulator by special assignment of subcarriers, thus allowing signal clipping at the zero level and avoiding the need for DC bias at the expense of data rate reduction. DCO-OFDM assigns data to all possible subcarriers to increase the data rate. However, half-wave symmetry signals cannot be achieved and a high DC bias is needed to convert the bipolar signal to a unipolar signal before modulating the LED intensity. This paper considers a practical LED model and studies the performance of both systems in terms of average electrical OFDM signal power versus bit error ratio in the presence of an additive white Gaussian noise (AWGN) channel. In addition, DC power consumption and the transmitted optical power for the two systems are compared. The analytical results are validated through Monte Carlo simulations and the obtained results demonstrate close match. It is shown that LED clipping has significant impact on the performance of both systems and an optimum system design should take into account the OFDM signal power, DC-bias point, and LED dynamic range.