Multi-photon polymer crosslinking evolves as the core process behind high-resolution additive microfabrication with soft materials for implantable/wearable electronics, tissue engineering, micro-robotics, biosensing, drug delivery, etc. Electrons and soft X-rays, in principle, can offer even higher resolution and printing rates. However, these powerful lithographic tools are difficult to apply to vacuum incompatible liquid precursor solutions used in continuous additive fabrication. In this work, using biocompatible hydrogel as a model soft material, we demonstrate high-resolution in-liquid polymer crosslinking using scanning electron and X-ray microscopes. The approach augments the existing solid state electron/X-rays lithography and beam induced deposition techniques with a wider class of possible chemical reactions, precursors and functionalities. We discuss focused beam crosslinking mechanism, the factors affecting the ultimate feature size and layer-by-layer printing possibilities. The potential of this technology is *