Clinton won an overwhelming majority of the delegates in Kentucky, but Obama was expected to fare better in Oregon, where the deadline to vote was 11 p.m. EDT.
Clinton won at least 37 delegates in the two states and Obama won at least 23, according to an analysis of election returns by The Associated Press. All 51 delegates from Kentucky were awarded but there were still 43 of 52 to be allocated in Oregon.
Obama has won 1,633.5 pledged delegates in primaries and caucuses, surpassing the 1,627 needed to claim a majority. There are three primaries remaining.
Obama has an overall total of 1,940 delegates, including endorsements from party and elected officials known as superdelegates. Clinton has 1,759, including superdelegates, according the latest tally by the AP.
Obama is expected to come out of the two contests about 60 delegates short of the 2,026 needed to clinch the nomination. He has added nearly that many superdelegates in the past two weeks.
Obama added two superdelegates Tuesday and Clinton picked up one.
Republicans also were voting in the two states, but Sen. John McCain clinched the GOP nomination in March.
The AP tracks the delegate races by calculating the number of national convention delegates won by candidates in each presidential primary or caucus, based on state and national party rules, and by interviewing unpledged delegates to obtain their preferences.
Most primaries and some caucuses are binding, meaning delegates won by the candidates are pledged to support that candidate at the national conventions this summer.
Political parties in some states, however, use multistep procedures to award national delegates. Typically, such states use local caucuses to elect delegates to state or congressional district conventions, where national delegates are selected. In these states, the AP uses the results from local caucuses to calculate the number of national delegates each candidate will win, if the candidate's level of support at the caucus doesn't change.