This paper concerns the monotone approximations of solutions of boundary value problems such as: -u' + f(t,u,u') = 0, u'(O) = u'(1) = 0. The author consider linear in.terative scheme in case f is Lipschitz in u' and satisfies a one sided Lipschitz condition in u. The initial approximations are lower and upper solutions which can be ordered one way alpha or or = beta. The author also consider the periodic and the Dirichlet problems.