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Jordan $H^{*}$-pairs appear, in a natural way, in the study of Lie $H^{*}$-triple systems ([3]). Indeed, it is shown in [4, Th. 3.1] that the problem of the classification of Lie $H^{*}$-triple systems is reduced to prove the existence of certain $L^{*}$-algebra envelopes, and it is also shown in [3] that we can associate topologically simple nonquadratic Jordan $H^{*}$-pairs to a wide class of Lie $H^{*}$-triple systems and then the above envelopes can be obtained from a suitable classification, in terms of associative $H^{*}$-pairs, of...