In 1979, the Bethesda home that Neal W. Cornell had just bought for $124,000 was valued by Montgomery County tax officials at $83,000. The annual tax on the house and land in the Bannockburn neighborhood was then $1,300. Cornell, a biochemist at the National Institutes of Health, figured it would stay constant for at least the next couple of years.

Not so. The very next year, after the passage of controversial legislation ordering local tax officials to assess all Maryland homes once every three years, Cornell's house was reassessed, this time for $129,000. Under that reassessment his 1982 property tax bill soared to $1,800; next year's tax will climb to roughly $2,000, Cornell said.

"On the one hand, the increase seems rather high because we made no major improvements, just some repainting and new gutters," said Cornell, who is president of the Bannockburn Civic Association. "But I guess the new assessment is a better reflection of the house's market value."

Cornell did not appeal his new assessment, but 3,265 other Montgomery County residents did by last week's filing deadline. With assessments up an average 30 percent since 1979 valuations, county assessors say homeowners are more bitter than ever about their notices, on which the county will later base individual property taxes.

In Prince George's County, officials also reported an increase in assessment appeals.

"People out there are really angry," said George M. Andrews, Montgomery County assistant supervisor of assessments, who was shouted down earlier this month when he met with residents of Bethesda's Whittier Woods neighborhood.

For about two hours, homeowners, some waving their assessment notices, pelted Andrews with pointed questions about their assessment increases. "I've seen friendlier groups before," Andrews said.

"The thing that makes it different this year is not so much the increases, but the impression that people have that property values have gone down," he said.

Homeowners believe that the assessments should more closely reflect the housing market slump, but ignore the fact that in some residential pockets of Montgomery the local market is impervious to the nationwide flattening of home prices, Andrews said.

"The danger is that people see what they want to see. In this county, you used to be unable to unload a house in a day or two, or in 30 to 60 days," he said. "Now you're looking at a year to unload your house. But that doesn't mean property values have gone down."

However, some local civic group leaders contend that if property values did not drop, they should have at least held steady over the past three years.

"It seems that in a depressed market, houses shouldn't have gone up as they did in some areas," said William Anderson, the new president of the Montgomery County Taxpayer's League, which keeps tabs on county spending.

One way to offset the rise in home values would be to lower the property tax rate--the major ingredient in the tax bill a homeowner receives, Anderson said.

Last week, Maryland Gov. Harry Hughes proposed to raise the state property tax from 21 cents to 24 cents per $100 of assessed value, a move that would add an annual $13.50 of tax on a home assessed at $100,000.

In Montgomery, the property tax now stands at about $3.60 per $100 valuation, depending on a community's local services, such as water, sewer and parks.

The most recent round of assessments affected the 70,000 homes and businesses included in the first year of the triennial system: half of Bethesda, Wheaton and Rockville and the entire Darnestown, Poolesville, Barnesville, Clarksburg and Damascus election districts.

This year's reassessments will affect half of Olney and Rockville and the entire Colesville, Gaithersburg and Laytonsville election districts.

"There are some very nice subdivisions in those areas assessed in 1982 that are not affected by the shortage of housing money," Andrews said. The assessment on his Barnesville area home jumped more than 45 percent since 1979, he said.

(Under the three-year schedule, homeowners stagger tax payments on each new assessment over three years; the state imposed a 15 percent limit on the amount of assessment increase that may be taxed in one year.)

Neighboring Prince George's County also has witnessed growing resentment by property owners over their own assessment hikes.

"Folks are definitely unhappy," said Thomas F. Houff, acting supervisor of the county's assessment office. "After all, it's a very visible tax. Uncle Sam takes tax out of your paycheck. We send out notices.

"We get a lot of questions about these increases, but the fact is, this is a change in a house's value over a three-year period."

In some ways, he said, Prince George's is worlds apart from Montgomery: Not only were property taxes capped in 1979, but the Prince George's assessments climbed an average of only 24 percent since 1979. The county's average tax rate is $3.40 per $100.

Prince George's sent out slightly fewer 1982 assessment notices than Montgomery--about 65,000 to residents of the Hyattsville, Mount Rainier, Takoma Park, Riverdale, College Park and Oxon Hill areas--and had 3,605 appeals, Houff said. Communities scheduled for assessments this year include those in a strip from Laurel south to Aquasco: Bowie, Upper Marlboro, Clinton and Brandywine.

Few appeals are successful, however. Houff and Andrews said a homeowner may have a one in five chance of winning an appeal.

One homeowner's appeal, successful before Montgomery's Property Tax Assessment Appeal Board and now being challenged by the state, could eventually reshape the triennial system of property assessments.

Stanley Racoosin, a lawyer who lives in Bethesda, appealed his 1979 assessment notice, saying the state had improperly applied the triennial assessment law. Racoosin argued that homes assessed in the system's second and third years enjoyed an unfair advantage over those evaluated in the first year.

"The way the county appplied the law wasn't uniform," he said last week. "There's an unfair burden on the people in the first group: Everybody else has their assessments frozen while we pay the higher rate."

The appeal board apparently agreed, ruling in Racoosin's favor in 1981. The state's appeal of that decision is pending before the Maryland Tax Court.