In this paper, a kind of generalized Sobolev-Wiener classes
$$W_{pq}^r ({\text{R}},h),h > 0$$
, h>0, defined on the whole real axis, is introduced, and the average σ-K width problem of these function classes in the metric
$$W_{pq}^r ({\text{R}},h),h > 0$$
is studied. For the case p=+∞, 1≤q≤+∞, the case 1≤p <+∞, q=1, we get their exact values and identify their optimal subspaces.