The molar excess volume V-E has been obtained trough the concentration range at 298.15 K for 41 systems composed of the series of glymes (oxaalkanes), CH3-O-(CH2-CH2-O)(m)-CH3 with n = 1 to 4 with normal, branched and cyclic alkanes. With literature values, a comprehensive view is given of (a) the change of equimolar V-E with the molecular sizes of the components and with alkane structure and (b) concentration dependences which are S-shaped for certain systems. Equimolar H-E were obtained at 303.15 K for 43 of the systems and used in applying the Prigogine-Flory (PF) theory to successfully predict the V-E features. Evidence for association (Hydrogen bonding) in the pure glymes is reviewed. This accounts for discrepancies between PF theory and experiment which are minor for V-E, but major for dV(E)/dT and C-p(E) as Seen through a consideration of literature values of these quantities.