Meeting in the shadow of the Republican Convention in Detroit, the Democrats open one of their biggest fights of the presidential year in Washington today -- over a loyalty rule aimed at keeping President Carter's delegates in line.

Carter has the backing of a majority on the Democrats' rules committee, which is expected to give approval to the loyalty rule at its preconvention session here.

Backers of Sen. Edward M. Kennedy, who is challenging Carter for the party nomination, have threatened a floor fight over the loyalty rule at the Democratic convention.

Defeating the rule might be the last hope for Kennedy, who cannot wrest the nomination from Carter without wooing away many of the delegates the president won in primaries and state conventions.

Carter's supporters say delegates have an obligation to reflect the feelings of those who elected them. But Kennedy supporters say delegates have a right to change their minds or to reflect changed feelings by their constitutions back home.

Several other items will come before the committee this week, including the question of whether to continue midterm conferences, or miniconventions, which the Democrats held in 1974 and 1978; whether to make equal representation for women at national conventions a permanent requirement; and whether to tighten the rules requiring presidential primaries and caucuses to be held during a 14-week span between March and June.