The aim of this paper is to study regularity for weak solutions to the nondiagonal quasilinear degenerate parabolic systems related to Hörmander's vector fields, where the lower order items satisfy controllable growth conditions. Higher Morrey regularity is proved by establishing a reverse Hölder inequality for weak solutions, and then Hölder regularity is obtained by the isomorphic relationship.

This work is supported by the National Natural Science Foundation of China (Grant Nos. 11701162); Natural Science Foundation Research Project of Shaanxi Province (Grant No. 2016JQ1029); Natural Science Foundation of Education Department of Shaanxi Provincial Government(Grant No. 16JK1320); Research Fund for the Doctoral Program of Hubei University of Economics (Grant No. XJ16BS28).