Summary: An example is given to show that the necessary conditions of Theorem 4.5 [in G. Y. Chen
et al. Math. Methods Oper. Res. 49, No. 2, 239–253 (1999; Zbl 0939.90014
)] and Theorem 2.1 (i) [in X. Q. C. J. Goh
and X. Q. Yang
, Eur. J. Oper. Res. 116, 615–628 (1999; Zbl 1009.90093
)] for (weak) vector equilibrium flows may not hold. New
-equilibrium and parametric equilibrium flows are introduced. As a result, necessary and sufficient conditions between a weak vector equilibrium flow and an
-equilibrium flow and between a vector equilibrium flow and a parametric equilibrium flow are established.