Serious crime in Alexandria declined by 5.8 percent in 1984, while in Arlington it fell by two-tenths of one percent, according to police in those neighboring jurisdictions.

The reported incidence of serious crime -- murder, rape, robbery, burglary, aggravated assault, larceny and vehicle theft -- has generally been dropping in the Washington area for the last three years, although the reduction in Alexandria was the fifth in five years.

Officials say the drop in part reflects a slowing crime rate nationwide attributed to the decline in the number of people under 25, the age group most likely to commit crimes.

Authorities in both Alexandria and Arlington also credited increased citizen awareness of crime and neighborhood watch programs with helping cut the crime rate.

In Arlington, where the number of rapes dropped from 67 in 1983 to 37 last year -- a decrease of 45 percent -- county police spokesman Randy Bertsch yesterday cited increased awareness on the part of potential victims prompted by news reports and television shows dealing with violence against women.

Arlington police, concerned about assaults on women, began a series of self-defense classes last fall, said Cpl. Carl Childress, who teaches the classes. He said he sees a need for the classes because "Arlington has a lot of single females living alone" and because the use of public transit rather than cars has increased pedestrian traffic.

In addition to the drop in Alexandria's crime rate, police there said the "clearance rate," or rate of cases closed by arrest or other means, increased to 20.5 percent, up one percentage point from 1983, Public Safety Director Charles T. Strobel reported.

A 15.5 percent decline in burglaries led the decrease in the figures in Alexandria, where 7,521 serious crimes were reported last year compared to 7,986 the year before. There were 1,531 burglaries committed in the city in 1984, down from 1,812. Robberies, larcenies, and aggravated assaults also were down.

Motor vehicle theft continued to plague the city. There were 631 motor vehicle thefts there in 1984, 121 (23.7 percent) more than in the previous year.

There were six homicides, the same number as in 1983, and all were closed. Rapes increased from 51 to 59, assaults were down by 2.3 percent and robberies declined by 6.2 percent.

Deputy Public Safety Director Arlen Justice said the department will place more emphasis this year on preventing auto thefts, particularly in the West End, which he calls a "supermarket for cars." Justice cited that area's proximity to Shirley Highway and the Capital Beltway and the large number of cars owned there by apartment dwellers as causes for the city's high auto theft rate.

In Arlington, the two-tenths of one percent decrease in serious crimes followed years in which the crime rate fell 17 percent, then 4 percent. "We may very well be running into a time when crime is maybe leveling out a little bit," Bertsch said.

The total number of serious crimes dropped from 7,614 in 1983 to 7,599 in 1984. The number of assaults, burglaries and vehicle thefts rose, while murders, robberies, larcenies and rapes decreased.

Police said they were not worried about a 5.2 percent increase in burglaries, from 1,382 in 1983 to 1,454 last year. "Burglaries have remained within a certain range. Of course, we'd like them to go down all the time," said Bertsch.