There is disclosed a control apparatus for operating any one of a plurality of parallel connected boilers as a lead boiler, with the others operating as lag boilers. The control apparatus enables a lag boiler to assist the lead boiler during a prolonged operating period to share the burden and the therefore prolong equipment life and increase system efficiency. The control apparatus enables each boiler to serve as the lead boiler while employing full modulation, other boilers such as the lag boiler also employ full modulation. The control apparatus also causes an automatic switch over between boilers after a malfunction of one of the boilers in a rapid time.