Summary: Methods of dynamical systems analysis are used to show rigorously that the presence of a magnetic field orthogonal to the two commuting Killing vector fields in any spatially homogeneous Bianchi type \(\text{VI}_0\) vacuum solution to Einstein’s equation changes the evolution toward the singularity from convergent to oscillatory. In particular, it is shown that the \(\alpha\)-limit set (for the time direction that puts the singularity in the past) of any of these magnetic solutions contains at least two sequential Kasner points of the Belinskii-Khalatnikov-Lifshitz sequence and the orbit of the transition solution between them. One of the Kasner points in the \(\alpha\)-limit set is non-flat, which leads to the result that each of these magnetic solutions has a curvature singularity.