If
(
Y
,
μ
)
(Y,\mu )
is an H-space then a measure of nonassociativity, called Homotopy Nuclear Nilpotency (HNN) is defined. We then calculate the HNN of thirteen H-spaces: the twelve classes of multiplications on
S
3
{S^3}
and the one class on
S
(
2
′
)
5
S_{(2’)}^5
, the 5-sphere localized away from 2.