What would happen if the pigeons in London suddenly hatched a generation of gryphons? The 16-page ""A Flock of Gryphons,"" one of the eight tidy pieces collected here, is Lively's fanciful speculation on the minor pandemonium and general gryphon fever that might result. A similar but smaller story describes the ""mushroom invasion"" that takes over the Hancock house when the children give their ""green-fingered"" mother a birthday gift of mushroom spores. In the title story, two children newly moved in an old house are pestered by a family of benign but bothersome resident ghosts. The children finally persuade the ghosts to move into a house with two babies, who are delighted by the ghosts' attention. In the end, then, everyone is happy. The opening story begins with a Martian coming to the door to borrow a spanner from Peter and Gran. ""Have a look in Grandad's toolbox,"" says Gran; and when the Martian's spaceship leaves without him (scared off by bullocks) she just as matter-of-factly takes hit in, knitting him a sweater, treating him to the village fete, and finally flashing ""torch"" signals until his ship returns. It's sort of like E.T. stiched on a tea cozy. In fact, all eight stories are cozy domestications of the supernatural, designed to curl up with rather than to curl hair. They are clever and polished, a bit precious, and very English, which may limit their appeal here.