WASHINGTON -- Many of the Republicans emerging as potential members of the Obama administration have professional and ideological ties to Brent Scowcroft, a former national-security adviser turned public critic of the Bush White House.

Mr. Scowcroft spoke by phone with President-elect Barack Obama last week, the latest in a months-long series of conversations between the two men about defense and foreign-policy issues, according to people familiar with the discussions.

The...