Martínez Alonso, LuisShabat, A. B.2023-06-202023-06-202003-051402-925110.2991/jnmp.2003.10.2.6https://hdl.handle.net/20.500.14352/51655©Atlantis Press. A B Shabat wish to thank A Ibort for his support during his stay as a visiting professor of the Carlos III University of Madrid. He also acknowledges the group of the Department of Theoretical Physics II of the Complutense University for their warm hospitality. L Martínez Alonso was partially supported by the DGCYT project BFM2002- 01607. A Shabat was partially supported by the RFFI project 01-01-00874 and Sc. Schools RF grant 06- 15-96093. Both authors are grateful to E Ferapontov for several useful and stimulating discussions.We present a theory of compatible differential constraints of a hydrodynamic hierarchy of infinite-dimensional systems. It provides a convenient point of view for studying and formulating integrability properties and it reveals some hidden structures of the theory of integrable systems. Illustrative examples and new integrable models are exhibited.engjournal articlehttp://dx.doi.org/10.2991/jnmp.2003.10.2.6http://www.tandfonline.comhttp://arxiv.org/abs/nlin/0310036open access51-73MathematicsappliedPhysicsmathematicalFísica-Modelos matemáticosFísica matemática