We study the asymptotic behavior of the solutions of the nonlinear Volterra integrodifferential equation \[ x ′ ( t ) + ∫ 0 t a ( t − s ) g ( x ( s ) ) d s = f ( t ) ( t ∈ R + ) . x’(t) + \int _0^t {a(t - s)g(x(s))\;ds\; = f(t)\quad (t \in {R^ + }).} \] Here R + = [ 0 , ∞ ) , a , g {R^ + } = [0,\infty ),a,g and f are given real functions, and x is the unknown solution. In particular, we give sufficient conditions which imply that x and x’ are square integrable.