THE Cottage has been in the same family for six generations. And its present inhabitants, if you believe the story, still include one or two from the past.

"There was the time we moved the portrait of my grandfather from upstairs to down. After we'd securely hung it, it fell off the wall. We took the hint, and put it back where it'd been," said Charles R. Hooff Jr., the present owner.

"Our granddaughter," said his wife, taking up the story, "one night was sleeping in the room with the portrait. She had a strong feeling someone was in the room -- and trying to get into bed with her. She thought it was the relative who had died in that bed years ago. She slept next door. We all hear it walking every so often, though old houses all have strange sounds.

"The music box in the attic played when our great aunt died, though it was old and dusty and no one had touched it in years. Sometimes the ghost turns out the lights -- once during a party. Still it's a nice ghost, it doesn't really do any harm."

We came into the Hooff house by the swimming pool. The Cottage was a farmhouse in the early 19th centruy, then a summer place when it acquired the dining wing and drawing room wings. The house still stands on three acres and the Hooffs are great gardeners. "In the summer, the flowers around the pool remind you of the tropics," said Mrs. Douglas Griffith Lindsey, tour chairman. The old defensive breastworks are behind the house. Old bullets and belt buckles turn up from time to time when the Hoofs are planting bulbs.

Inside the front door, on the right, we saw a tiny bay room, just big enough for a soft settee and the 3 1/2-year-old granddaughter, Elizabeth Janey Hooff. "Our firecracker, born on the Fourth of July, 1976," explained Hooff. The small room has sheer curtains, tied twice in a balloon effect by the clever Liz Hooff. The old floor has well-worn boards.

The family sometimes as a joke calls the parlor the "morgue" -- because it was so used during the War Between the States. The parlor displays Liz Hooff's family inheritance, a handsome Philadelphia highboy (much coveted by Clement Conger, another Alexandrian, for the White House, where he's curator).

One staid-looking wing chair, Mrs. Hooff is amused to reveal, was designed to hold what she called "a potty." Chinese Export porcelain lines the shelves. The desk is a fine Centennial copy of an early piece. The sofa belonged once to the Seminary.

Down the hall to the red-walled sitting room we went to see a cupboard full of old glass. In the other sitting room, across the hall, are more of the fine family portraits that are the glory of the house. Two are by Charles Bird King, famous for his Indian pictures. A portrait in the hall is of Sarah Caryle Fairfax Herbert Hooff, the present owner's mother, a formidable lady who is credited with sparking the restoration of Old-Town Alexandria in the 1930s. She began the real-estate firm that her son carried on, which is now headed by her grandson.

The dining room has a wonderful old claw-foot table. The drapery here is particularly nice around the windows, leaving the view of the garden clear.

The cottage is almost a sampler of Seminary Hill pleasures: old family house, old family portraits and furniture, and seeds planted by one generation to mature for the next.