For a finite, complete and positive measure space \((\Omega,\Sigma,\mu)\) and Banach spaces \(X\) and \(Y\) over the real or complex field, mappings \(U\) from \(\Omega\) into \(W(X,Y)\), the space of weakly compact operators from \(X\) to \(Y\), are considered. It is shown, if \(U\) is strongly integrable and \(U\) is uniformly norm bounded, that the integral operator \(\int_ \Omega U(\omega)(.)d\mu(\omega)\) is again weakly compact.