Continental Illinois Corp., its succession ranks decimated by firings and resignations in the wake of the Penn Square National Bank failure last year, this week elevated two top officials, making them the leading candidates to be the bank's next chairman and president.

The bank announced that David G. Taylor, the executive vice president in charge of the bank's bond department, had been named a vice chairman of the bank company, while the executive vice president in charge of the trust department, Edward S. Bottum, will become the bank's chief lender.

Neither Taylor nor Bottum was touched in the Penn Square scandal, which forced the resignation of the bank's former chief lending officer, George R. Baker, who had been considered the leading candidate to succeed chairman Roger Anderson, 62. Now Taylor, 54, is expected to succeed Anderson when he retires in 1986.

President John H. Perkins also is 62, while vice chairman Donald C. Miller is 63. Thus the entire top management of the bank will change within three years. Bottum, 50, is the leading candidate to succeed Perkins, sources said.

Continental Illinois, which owns the nation's seventh biggest bank, has been reeling for more than a year as a result of hundreds of millions of dollars of bad loans it bought from the Penn Square National Bank. Bank earnings have been hit hard. Morale is low as the once aggressive bank--it was the nation's largest corporate lender--retrenches in the face of the Penn Square fiasco and the lingering effects of the general recession.

The appointments of Taylor and Bottum "should ease some of the questions of leadership down the road," said a bank official.

Anderson said the appointments were "appropriate at this time as our organization focuses on the strategic plans that will carry us beyond my planned retirement date in 1986."