According to economic theory, equilibrium happens in every market structure (in the long run) so long as the government does not set a price floor or a price ceiling. Therefore, equilibrium is necessary in a market that is an oligopoly as long as the price of the good or service is allowed to move freely.
When economists speak of market equilibrium, they are speaking about the situation in which the quantity supplied and the quantity demanded are the same. This situation occurs at a particular price level. At that price, the amount of the product that the suppliers provide and that consumers demand is the same and the market is said to be in equilibrium.
As long as the price is free to move, equilibrium will be reached because suppliers will change their prices if needed. If there is a market surplus, they will lower their prices. If there is a market shortage, they will raise their prices. In these ways, equilibrium will always be reached in an oligopoly where the price is free to move.