Let A be an algebra such that exactly algebras isomorphic to a retract of A can be constructed from A by direct limits. Then A is said to be an algebra with easy direct limits. We will prove that if A is a monounary, then A is countable and the number of retracts of A is not equal to @ 0. Further, we will see that the number of non-isomorphic monounary algebras with easy direct limits is 2 @ 0 .