By introducing spinor currents in addition to the algebra of vector and axial-vector currents, new symmetries of hadrons are obtained in which both baryons and mesons are grouped together in a supermultiplet. These currents are constructed as bilinear combinations of fundamental fields, both bosonic and fermionic. They form a generalized Jordan algebra, whose representations are constructed. As possible models, two examples are given, V(6,3) and V(6,21). In the latter, all known hadrons are included in the adjoint representation.