Three days after her reelection to the Virginia House of Delegates, Arlington's Mary A. Marshall has embarked on another campaign.

She wants to become the first woman to hold a key leadership position in the 100-member House of Delegates and has begun soliciting votes in an effort to oust a cigar-chomping, six-term House member as chairman of the 74-member House Democratic caucus.

If Marshall succeeds, she will be the only Northern Virginian to occupy a leadership position in the House. In announcing her campaign against Del. C. Hardaway Marks (D-Hopewell), Marshall, 58, first elected the General Assembly in 1966, cited the need for "more orderly procedures" during House caucuses.

Her effort to move from her current job as secretary of the caucus comes as House faces a major leadership shake-up with the pending retirement of longtime Speaker John Warren Cooke. House Majority Leader A.L. Philpott (D-Henry) is certain to succeed Cooke, but there is a scramble for the majority leader's job.

At the same time, there have been repeated suggestions that Senate Democratic conservatives may attempt to oust Sen. Adelard L. Brault of Fairfax as the party's majority leader in that chamber. Sen. Hunter B. Andrews (D-Hampton), who opposed Brault's bid four years ago, recently called such reports "crap" but he stopped short of ruling out his candidacy.

Brault could not be reached for comment yesterday.

Should Marshall oust Marks, she would become the first Northern Virginian to hold a leadership role in the House since the defeat of Del. james M. Thomson (D-Alexandria) in 1977.

Thomson was House majority leader and in like to succeed Cooke until his defeat two years ago.

Del. Dorothy S. McDiarmid (D-Fairfax) said yesterday that Marshall telephoned her recently about challenging Marks. "Mary told me she thinks she can do a good job as a chairman," McDiarmid said. "She's a very able person and I told her I'd support her."

Prospects for Marshall's election probably were dimmed by Tuesday's elections when the number of Democrats in the Northern Virginia delegation dropped to 10, a loss of three to Republicans. Voting along sectional lines often is a key factor in house elections.