Thenonabelian tensor square G[otimes] G of a group G is generated by the symbolsg[otimes] h, g,h ∈ G, subject to the relations$$gg\prime\otimesh=(^gg\prime\otimes^gh)(g\otimesh) andg\otimeshh\prime-(g\otimesh)(^hg\otimes^hh\prime),$$ for all $g,g\prime,h,h\prime\in G< / f>, where $^gg\prime=gg\primeg^{−1}$. The nonabelian tensor squareis a special case of the nonabelian tensor product which has its origins inhomotopy theory. It was introduced by R. Brown and J.-L. Loday in [4]and [5], extending ideas of J.H.C. Whitehead in [10]. The topicof this paper is the classification of 2-generator 2-groups of class two up toisomorphism and the determination of nonabelian tensor squares for thesegroups.