[en] Previous results for nuclear fluxes during coherent tunnelling of molecules with symmetric double well potentials are extended to fluxes in asymmetric double well potentials. The theory is derived using the two-state approximation (TSA). The symmetric system serves as a reference. As an example, we consider the one-dimensional model of the tunnelling inversion of oriented ammonia, with semiclassical dipole coupling to an electric field. The tunnelling splitting increases with the dipole coupling by a factor $f⩾<!--\; ???\; -->1.$ The tunnelling time decreases by $1/f.$ The nuclear density appears as the sum of two parts: The tunnelling part decreases as ${1/f}^2$ times the density of the symmetric reference, whereas the non-tunnelling part is the initial density times $\left({1-<!--\; ???\; -->1/f}^2\right).$ Likewise, the nuclear flux decreases by $1/f,$ with essentially the same shape as for the symmetric reference, with maximum value at the potential barrier. Coherent nuclear tunnellings starting from the upper or lower wells of the asymmetric potential are equivalent. The results are universal, in the frame of the TSA, hence they allow straightforward extrapolations from one system to others. This is demonstrated by the prediction of isotope effects for five isotopomers of ammonia. (special issues/sections)