In this paper we consider the following nonlocal boundary value problems (p(t)x')'=f(t,x,x'), x'(0)=∣0, x(1)=∫10 x'(s)dg(s) and (p(t)x')'=f(t,x,x'), x'(0)=0, x(1)=∫10 x(s)dg(s), where f:[0,1]×Rk×Rk → Rk and the integrals are meant in the sense of Riemann-Stieltjes. Under a sign condition on the function f , we prove the existence of solutions