In this paper, we consider the following second order ordinary differential equation:(1.1)x''=f(t,x(t),x ' (t))+e(t),t (0,1),subject to one of the following boundary value conditions:(1.10)x(0)=αx(ξ),x(1)= j = 1 n - 2 β j x(η j ),(1.11)x(0)=αx( ξ),x ' (1)= j = 1 n - 2 β j x ' (η j ),(1.12)x ' (0)=αx ' (ξ),x(1)= j = 1 n - 2 β j x(η j ),(1.13)x ' (0)=αx ' (ξ),x ' (1)= j = 1 n - 2 β j x ' (η j ),w here α,β j (1=<j=<n-2) R, 0<η 1 <η 2 <...<η n - 2 <1, 0<ξ<1. When all the β j 's have no same sign, some existence results are given for (1.1) with boundary conditions (1.10)-(1.13) at resonance case. We also give some examples to demonstrate our results.