The second will be a larger, one-off global campaign, details of which have not yet been released to agencies. It is also expected to concern fuel.
The pitch is being run by John Payne, the company's head of marketing services and procurement.
On Tuesday this week, BP announced a 1.5 per cent increase in its second-quarter profits to £3.5 billion compared with a similar period in 2006. Its revenue for the quarter fell slightly from £35.71 billion to £35.65 billion. BP blamed a fall in production and lower cash flow for the "modest" decrease.
BP Ultimate is the company's premier fuel, and was designed to give improved vehicle performance and increased mileage.
The decision to pitch the two digital briefs follows the company's appointment of Chemistry Communications to handle its "Target Neutral" direct marketing campaign.
The initiative, which asks drivers to pay to offset the impact of their vehicles' CO2 emissions, is a non-profit programme that is run by a number of non-governmental organisations in partnership with BP.