Homicides and rapes declined last year in Montgomery and Fairfax counties, but robberies, larcenies and auto thefts increased in both of these growing and affluent suburban jurisdictions, police reported yesterday.

Robberies in Fairfax were up 15.6 percent, from 442 in 1984 to 511 last year, while Montgomery robberies rose 14.2 percent, from 591 to 675. At the same time, rapes dropped 16.8 percent, from 137 to 114, in Montgomery and by 7 percent, from 61 to 57, in Fairfax.

In Fairfax, despite numerical increases in some categories, police said the rate of violent crime of 141.7 per 100,000 residents was virtually unchanged from 1984. "The bright spot," said Col. John E. Granfield, Fairfax police chief, was the fifth straight decline in burglaries.

The most recent drop, from 3,285 to 3,213, "is of greater significance than those numbers indicate because the number of housing units increased by nearly 10,000 from 1984 to 1985."

Also taking a long-term view, Montgomery Police Chief Bernard Crooke said, "Crimes against persons are 30 percent higher than they were a decade ago, and I think that reflects the changes in the county . . . . Sixty percent of the people who work in the county now live in the county, and the daylight population increases."

In Fairfax, meanwhile, the number of crimes against people has stayed the same, police said. In "the crime you really want to worry about, against people, we feel we're holding our own," said Warren R. Carmichael, the department spokesman.

But larcenies registered the largest numerical increase in Fairfax, from 15,499 to 17,408; and car thefts rose from 1,265 to 1,509. In Montgomery, larcenies were up from 15,156 to 16,177, and car thefts were up from 1,552 to 1,900. "The reasons for that are that the targets of opportunity have increased," said Carmichael. "The county is expanding in so many different ways . . . . When there is more property out there . . . that's an additional target."

Similarly, in Montgomery, officials noted more thefts where there are daytime concentrations of parked cars, such as the Shady Grove Metro parking lot. Crooke said the department plans to produce a handout "that looks like a ticket" to place on windshields "to educate them to protect their valuables."

Violent crimes increased most in the Wheaton-Glenmont and Germantown districts, reflecting, officials said, changes in the county. "Where we're experiencing most of the crime are the areas where we're seeing the most growth," said Crooke.

In other categories, Montgomery also reported increases in crimes of vice and prostitution, up 120 percent; narcotics, up 8.8 percent; and child abuse, up 21.3 percent.