Finding optimal operating modes for bioprocesses has been, for a long time, a relevant issue in bioengineering. The problem is of special interest when it implies the simultaneous optimization of competing objectives. In this paper, we address the problem of finding optimal steady states that achieve the best tradeoff between yield and productivity by using nonmodel - based extremum-seeking control with semiglobal practical stability and convergence properties. A special attention is paid to processes with multiple steady states and multivalued cost functions. (C) 2009 American Institute-of Chemical Engineers Biotechnol. Prog., 25: 683-689, 2009