Answer: It sounds like you could have an infestation of fungus gnats, which lay eggs in the soil. In small numbers, the insect is merely a nuisance. The larvae, however, devour young roots, and a severe infestation can harm plants.
Any house plant pests can be brought into your home on new plants. They can also come inside with your plants after a summer in the garden. Fungus gnat seem to come out of nowhere, and appear on houseplants and seedlings.
One control is called Knock-Out Gnats (available from Gardens Alive, ph# 812-537-8650, address 5100 Schenley Pl., Lawrenceburg, IN 47025); this product contains a strain of Bt, a biological control, that controls the larvae.
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