Using the properties of almost nonexpansive curves introduced by B. Djafari Rouhani, we study the asymptotic behavior of solutions of nonlinear functional differential equation d u ( t ) / d t + A u ( t ) + G ( u ) ( t ) ∋ f ( t ) , where A is a maximal monotone operator in a Hilbert space H , f ∈ L 1 ( 0 , ∞ : H ) and G : C ( [ 0 , ∞ ) : D ( A ) ¯ ) → L 1 ( 0 , ∞ : H ) is a given mapping.