In this paper, I consider Lyapunov functionals combined with the Laplace transform to obtain boundedness results regarding the solutions of the nonlinear Volterra integro-differential equationsx′(t)=A(t)x(t)+B(t)+∫0tC(t,s)f(x(s))ds+g(x(t)).Asymptotic stability results regarding the zero solution are carried out for the case where B(t) is identically zero. Numerical examples are proposed to perform the given results.