A sequential approach to sparse component analysis (SeqTIF) is proposed in this paper. Although SeqTIF employs the estimation process of the simultaneous TIFROM algorithm, a source cancellation and deflation technique are also incorporated to sequentially estimate speech signals in the mixture. Results indicate that SeqTIF's separation performance shows a clear improvement upon the simultaneous TIFROM approach, due to the less restrictive assumptions it places upon the signals in the mixture. In particular, the analysis indicates SeqTIF's data efficiency is high, enabling the sequential approach to track a time-varying mixture with much greater accuracy than the simultaneous algorithm. Furthermore, SeqTIF is a more flexible approach, free from the constraints that a simultaneous approach places upon the mixing system.