In the study of Sobolev orthogonal polynomials, corresponding to the inner product
where and are distribution functions and , an essential role has been played by the concept of coherence. If and are monic orthogonal polynomial sequences corresponding to and , respectively, then is a coherent pair if
This concept can be extended to quasi-definite linear functionals and . When and are coherent, the Sobolev polynomial sequence has a structure suitable for further study. Nevertheless, it is important to know all the coherent pairs precisely, and this is the aim of this paper. The author proves that if is a coherent pair, then at least one of the functionals is classical (Hermite, Laguerre, Jacobi or Bessel). Moreover, all the coherent pairs are given explicitly. Analogous results are established for symmetric coherent pairs, when the subindices involved in the r.h.s. of (*) are and .