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The president-elect praised Mr. Bush for helping with a smooth transition of power, and recalled George Washington taking the first presidential oath of office in 1789.

“Since then, Inaugurations have taken place during times of war and peace; in Depression and prosperity. Our democracy has undergone many changes, and our people have taken many steps in pursuit of a more perfect union. What has always endured is this peaceful and orderly transition of power,” Mr. Obama said.

He recorded the address this week and released it at 6 a.m.

In his parting radio address Mr. Bush said Mr. Obama’s inauguration is a continuation of the “simple dream of dignity” he spoke about in his own 2001 inauguration.

Mr. Bush cautioned Americans to think of the world in terms of good and evil and not to be afraid to take sides in battle between the two.

“Good and evil are present in this world, and between the two there can be no compromise,” he said, reprising part of his farewell address from Thursday night.

Mr. Bush has continued the tradition of delivering a radio address every week, which is usually taped late in the work week and released on an embargoed basis to be broadcast just after 10 a.m. on Saturday mornings.

At times he has used the address to make policy, and has occasionally deviated from the taped format to deliver a live address, such as on Dec. 17, 2005, when he spoke live from the Oval Office to call for renewal of the Patriot Act.

In signing off Saturday morning, Mr. Bush said he looks forward to returning to Texas on Tuesday.

“I will depart office proud of my Administration’s record. And I will spend the rest of my life grateful for the opportunity to have served as President of the greatest nation on Earth.”