Let m, n, s be positive integers. Let \(\mathcal{F}\mathcal{M}_{m,n}\) denotes the category of fibered manifolds with m-dimensional bases and n-dimensional fibres and their fibered local diffeomorphisms. We prove that if \(m\ge 3\) then any \(\mathcal{F}\mathcal{M}_{m,n}\) -natural operator C transforming pairs \((\lambda ,X)\) of Lagrangians \(\lambda :J^sY\rightarrow \bigwedge ^mT^*M\) on \(\mathcal{F}\mathcal{M}_{m,n}\) -objects \(Y\rightarrow M\) and vector fields X on M into Euler maps \(C(\lambda ,X):J^{2s}Y\rightarrow V^*Y\otimes \bigwedge ^m T^*M\) on Y is of the form \(C(\lambda ,X)=cE(\lambda )\) , \(c\in \textbf{R}\) , where E is the Euler operator. We also prove that if \(m\ge 2\) and \(n\ge 2\) , then any \(\mathcal{F}\mathcal{M}_{m,n}\) -natural operator D transforming tuples \((\epsilon ,X)\) of Euler maps \(\epsilon :J^sY\rightarrow V^*Y\otimes \bigwedge ^mT^*M\) on \(\mathcal{F}\mathcal{M}_{m,n}\) -objects \(Y\rightarrow M\) and vector fields X on M into Helmholtz maps \(D(\epsilon ,X):J^{2s}Y\rightarrow V^*J^sY\otimes V^*Y\otimes \bigwedge ^m T^*M\) on \(Y\rightarrow M\) is of the form \(D(\epsilon ,X)=cH(\epsilon )\) for a real number c, where H is the Helmholtz operator.
