In a bilateral monopoly there is both a monopoly (a single seller) and monopsony (a single buyer) in the same market.
In such, market price and output will be determined by forces like bargaining power of both buyer and seller. A bilateral monopoly model is often used in situations where the switching costs of both sides are prohibitively high.
Bilateral monopoly situations are commonly analyzed using the theory of Nash bargaining games.
An example of a bilateral monopoly would be when a labor union (a monopolist in the supply of labor) faces a single large employer in a factory town (a monopsonist).