BAM and Laing O'Rourke are the two firms left in Coventry City Council's £355m Building Schools for the Future programme, after Sir Robert McAlpine was eliminated.
The BSF programme will involve building nine new schools and refurbishing 11 others as part of the national programme of upgrading state secondary schools.
A preferred bidder is expected to be announced in October with work starting on the first two school sites – subject to planning permission – in February 2011.
The first schools delivered through the programme are planned to open in the autumn of 2012.
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