Let f be a nonconstant meromorphic function in the complex plane. Nevanlinna theory asserts that f has a countable set of deficient values with total deficiencies at most 2. \textit{R. Nevanlinna} proposed (Le théorème de Picard-Borel et la théorie des fonctions méromorphes (1929)) to generalize this result in replacing complex values by meromorphic functions a(z) satisfying the condition \(T(r,a)=o(T(r,f))\) and solved it in the case of \(q=3\). \textit{C. Chuang} [Sci. Sin. 13, 887- 895 (1964; Zbl 0146.102) gave a positive answer when f is entire. The reviewer [Sci. Sin. 24, 1179-1189 (1981; Zbl 0466.30023)] showed that if the lower order \(\mu\) of f is finite, then f has at most a countable number of deficient functions and the total deficiencies has an upper bound depending only on \(\mu\). This paper proves that f has at most a countable number of deficient rational functions with total deficiencies at most 2. The proof is clever to consider the Wronskian of 1, z, \(z^ 2,...\), \(z^{n+k-1}\), f(z), \(zf(z),...,z^ kf(z).\) In the general case, \textit{C. F. Osgood} (preprint) obtained a complete result by number theoretical methods and \textit{N. Steinmetz} (preprint) subsequently gave a short and wise proof which was influenced by this paper.