Since that time Ukraine has consistently followed a course towards nuclear-weapon-free status . One of the first significant steps in this direction was the signature of the Lisbon Protocol to the Treaty on Strategic Offensive Arms ( START I ) ( May 1992 ) , according to which Ukraine assumed the obligations of the former Soviet Union under the aforementioned Treaty and pledged to accede to the Treaty on the Non-Proliferation of Nuclear Weapons as a non-nuclear-weapon State .