Organized labor is watching uneasily as two measures important to unions move through Congress.
* The Senate this week unanimously approved a bill that would require union officials to leave office as soon as they are convicted of major crimes. Now union officials may continue to hold office until all appeals are exhausted, often for a year or longer.
* The House Energy and Commerce committee approved 25 to 17 a bill requiring that all automobiles and trucks sold in the United States contain a specificed percentage of parts and components made in this country. This is the ''domestic content'' measure backed by the United Automobile Workers and other industrial unions, but opposed by the Reagan administration.
The domestic content bill has wide support in labor, although some unions fear that its passage - far from assured - could lead to retaliation overseas and threats to jobs for some workers who produce goods for overseas markets.
The Reagan administration has opposed the measure as one that might upset trade relations. Supporters say the bill is intended to force Japanese and other foreign auto producers to establish factories in this country.
The bill now goes to the House Ways and Means Committee for a 30-day study of its tariff implications. It is expected to reach the House floor ''some time after Labor Day.'' If passed by the House, the legislation faces trouble in the Senate. Rep. Dennis E. Eckart (D) of Ohio, one of the bill's most ardent backers , concedes that it has ''little chance in the Senate'' this session.
The anticorruption bill passed by the Senate 75 to 0 on June 20 was not widely opposed by the unions. It applies to elected union officials and financial officers, such as pension fund trustees, and to management officers who deal with unions. The Senate passed similar bills twice in 1982, but each time the measures died in the House. The bill is now headed toward a third House vote with better prospects for adoption.
The Senate vote this week is primarily a reaction to the conviction of Roy L. Williams, resigned president of the International Brotherhood of Teamsters, and others tied to the IBT, on charges of attempted bribery of former Sen. Howard W. Cannon of Nevada.
Mr. Williams agreed to give up the IBT presidency in a federal court deal that allowed him to remain free on bail during appeals. He has been seriously ill.
Jackie Presser, named to succeed him in the presidency, recently has been involved in investigations of local union payroll irregularities. He says that he has been vindicated in past probes and will be again.
Sen. Orrin G. Hatch (R) of Utah, chairman of the Senate Labor Committee, says that Justice Department records indicate a need for stronger anticorruption laws. Justice has reported 136 union officials convicted under federal fine laws in 1981 and '82.
Although Lane Kirkland of the AFL-CIO and most unions support the anticorruption measure, many are wary of the possibility that it might be used as an antiunion weapon in major union disputes.