Construction of 24 state highway and bridge rehabilitation projects in Montgomery and Prince George's counties is expected to begin later this year, according to Eugene T. Camponeschi, the state department of transportation's district engineer for the two counties. Another 20 projects will get under way in 1983.

State officials added 62 resurfacing, bridge rehabilitation and highway safety projects throughout the state, costing $42.2 million, to the transportation department budget after the General Assembly approved a two-cent increase in the gasoline tax. The new work was added to the 162 projects, costing nearly $330 million, provided for in the highway program planned before the tax was voted this spring.

Camponeschi said the additional road projects, which will include resurfacing, lane construction, drainage, landscaping, improving railroad crossings, traffic control, building a ride-sharing facility and other improvements, are classified as special projects.

He said work on major projects, many of which involve bridge improvements, will cause some traffic delays that will inconvenience commuters. Construction will begin within four to six months after the projects are advertised for bidding, he said, and will take from a year to a year and a half to complete in most cases. The major work in Montgomery County will include:

* Maryland Rte. 198 (Spencerville Road)--Widen to four-lane highway from intersection with U.S. 29 to I-95 (two miles). The work should be completed within 1 1/2 to two construction seasons (four to six months), and will be advertised in January 1983. The project will cost $6.725 million.

* Maryland Rte. 28--Widen and rehabilitate bridge over I-270 (Washington National Pike). Lanes will not be closed down, but traffic will move slowly. It will be advertised next month. $3.214 million.

* U.S. Rte. 29 (Columbia Pike)--Replace bridge deck over Maryland Rte. 650. It will be advertised in December. $1.636 million.

* Maryland Rte. 28 (Dickerson Beallsville Road)--Resurfacing and safety improvement from Maryland Rte. 117 to Frederick County (7.93 miles). This work is expected to take one construction season. Camponeschi said a construction season can overlap from one year to the next, depending on weather and other factors. The project will be advertised this month. $2.377 million.

* Maryland Rte. 124 (Laytonsville Road)--Resurfacing and safety improvements from Fieldcrest Road to Brink Road. Major traffic problems are expected. Work may include drainage improvements and the addition of guard rails, and will be advertised in July. $1.170 million.

Major projects in Prince George's include:

* I-95 (Capital Beltway)--Replace bridge deck, or surface, on Woodrow Wilson Bridge. Camponeschi said this is a "very big project" and involves the complete redecking of the bridge. Traffic flow will be reduced from three lanes to one lane in both directions and Camponeschi expects "major traffic problems" on this job. He advised commuters to use another route during construction, which he estimated would take from two to two and a half years. It was advertised in April. $42.478 million.

* U.S. Rte. 50 (John Hanson Highway)--Replace bridge deck over Maryland Rte. 556 and over Folly Branch. Camponeschi said that Rte. 50 has been added to the interstate highway system and that this project will help provide for future lanes. It will be advertised in October. $5.515 million.

* U.S. Rte. 50--Replace bridge deck over Maryland Rte. 704. This work iompleted. It will be advertised in November. $2.794 million.

* I-95 (Capital Beltway)--Resurfacing and safety improvements from Maryland Rte. 214 to U.S. 50 (3.76 miles). Camponeschi said resurfacing the Beltway here is "very sorely needed" and that he hopes the work will be completed within four to six months. It will be advertised in August. $2.600 million.

* Maryland Rte. 410 (East-West Highway)--Replace bridge deck over northwest branch. Four-lane traffic will be maintained during construction, which should take from one and a half to two years. It will be advertised this month. $1.249 million.

Other Montgomery work will include:

* Maryland Rte. 187 (Old Georgetown Road)--Construct right turn lanes at Rockspring Drive. This work should not greatly inconvenience motorists, Camponeschi said, and will be advertised in July. $40,000.

* Maryland Rte. 28 (Darnestown-Rockville Road)--Widen to four lanes and construct left turn lane from I-270 to Research Boulevard (.34) miles. Work is estimated to take one construction season and will be confined to "non-peak" hours. It will be advertised in July. $500,000.

* Maryland Rte. 355 (Wisconsin Avenue)--Signal improvements, left turn lane onto Bradley Boulevard. Traffic flow will be maintained, and the project will be advertised in September. $39,000.

* Maryland Rte. 182 (Layhill Road)--Resurfacing and safety improvements at Indian Spring Road (bypass lane). Community residents asked for this work, which will take less than half a construction season to complete. It will be advertised next January. $108,000.

The B&O Railroad crossing at Maryland Route 185 (Connecticut Avenue) near Chevy Chase will be reconstructed. Work will be done in cooperation with the railroad company and the surface will be changed from blacktop to a smoother rubberized material. Traffic flow will be maintained and work should take four to six months. It will be advertised in September. $127,000.

Other Prince George's work will include:

Maryland Rte. 193 (University Boulevard)--Reconstruct signal at Maryland Rte. 650. Work should take a couple of months, and project will be advertised this month. $236,000.

* Maryland Rte. 201 (Kenilworth Avenue)--Widen westbound ramp and install signal at I-95 westbound ramp and Crescent Street. Work should be done in less than six months, and will be advertised in August. $185,000.

* Maryland Rte. 450 (Annapolis Road)--Widen to add double left turn lane at Princess Garden Parkway. It will be advertised in December. $198,000.

Camponeshi said that without the additional gasoline tax revenues, many of these projects would have been delayed another one to two years. He emphasized that in most cases work will be confined to non-peak hours.