The SII model in its present form (ANSI S3.5-1997, American National Standards Institute, New York) can accurately describe intelligibility for speech in stationary noise but fails to do so for nonstationary noise maskers. Here, an extension to the SII model is proposed with the aim to predict the speech intelligibility in both stationary and fluctuating noise. The basic principle of the present approach is that both speech and noise signal are partitioned into small time frames. Within each time frame the conventional SII is determined, yielding the speech information available to the listener at that time frame. Next, the SII values of these time frames are averaged, resulting in the SII for that particular condition. Using speech reception threshold (SRT) data from the literature, the extension to the present SII model can give a good account for SRTs in stationary noise, fluctuating speech noise, interrupted noise, and multiple-talker noise. The predictions for sinusoidally intensity modulated (SIM) noise and real speech or speech-like maskers are better than with the original SII model, but are still not accurate. For the latter type of maskers, informational masking may play a role.