Summary: For cohomological (respectively homological) coefficient systems \(\mathcal F\) (respectively \(\mathcal V\)) on affine buildings \(X\) with Coxeter data of type \(\widetilde A_d\), we give for any \(k\geq 1\) a sufficient local criterion which implies \(H^k(X,\mathcal F)=0\) (respectively \(H_k(X,\mathcal V)=0\)). Using this criterion we prove a conjecture of de Shalit on the acyclicity of coefficient systems attached to hyperplane arrangements on the Bruhat-Tits building of the general linear group over a local field. We also generalize an acyclicity theorem of Schneider and Stuhler on coefficient systems attached to representations.