  The notions of a box family and fibred cofinitely-coarse embedding are
introduced. The countable, residually amenable groups satisfying the Haagerup
property are then characterized as those possessing a box family that admits a
fibred cofinitely-coarse embedding into a Hilbert space. This is a
generalization of a result of X. Chen, Q. Wang and X. Wang on residually finite
groups.
