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We establish an invariant local trace formula for the tangent space of somesymmetric spaces over a non-archimedean local field of characteristic zero.These symmetric spaces are studied in Guo-Jacquet trace formulae and ourmethods are inspired by works of Waldspurger and Arthur. Some other results aregiven during the proof including a noninvariant local trace formula, Howe'sfiniteness for weighted orbital integrals and the representability of theFourier transform of weighted orbital integrals. These local results areprepared for the comparison of regular semi-simple terms, which are weightedorbital integrals, of an infinitesimal variant of Guo-Jacquet trace formulae.

A local trace formula for $p$-adic infinitesimal symmetric spaces: the case of Guo-Jacquet