Thermoplastic elastomer vulcanizate comprising: - a first phase based on at least one thermoplastic polymer chosen from the group consisting of homopolymers and copolymers of olefins, polyamides, polyimides (Pis), polyphthalamides (PPAs), polyetherimides (PEIs), polyamide-imides (PAIs), thermoplastic elastomers (TPEs) and blends thereof, said at least one thermoplastic polymer being comprised in the thermoplastic elastomer vulcanizate according to a weight fraction ranging from 20% to 80%; - a second phase based on at least one two-component (B1 and B2) liquid silicone elastomer crosslinked by hydrosilylation which comprises a first component comprising a mixture of diorganopolysiloxanes, a reinforcing silica and a platinum-based hydrosilylation catalyst, and a second component comprising a diorganopolysiloxane, an organohydridosilicone compound, a reinforcing silica and an inhibitor, said at least one liquid silicone elastomer being comprised in the thermoplastic elastomer vulcanizate according to a weight fraction ranging from 20% to 80%; and - a system for compatibilizing these phases together, characterized in that said system comprises: - at least one polymer chosen from the group consisting of grafted polyolefins, terpolymers containing poly(vinylaromatic/conjugated diene/methyl methacrylate) blocks, terpolymers containing poly(methyl methacrylate/alkyl acrylate/methyl methacrylate) blocks, ethylene/alkyl-(meth)acrylate/acrylic acid terpolymers and polymers resulting from at least one glycidyl ester such as ethylene/(meth)acrylate/glycidyl (meth)acrylate terpolymers; and - a polyorganosiloxane with SiH functional group(s), and in that said thermoplastic elastomer vulcanizate forms a homogeneous dispersion of said first and second phases obtained by reactive extrusion with at least the second phase which is continuous therein, said first phase being a discontinuous phase formed of nodules dispersed in said continuous second phase, or else the first and second phases being co-continuous in said thermoplastic elastomer vulcanizate in the form of nodules of one contained in the other and vice versa, these nodules having, in both cases, a mean size of less than 10 μm. - a first phase based on at least one thermoplastic polymer chosen from the group consisting of homopolymers and copolymers of olefins, polyamides, polyimides (Pis), polyphthalamides (PPAs), polyetherimides (PEIs), polyamide-imides (PAIs), thermoplastic elastomers (TPEs) and blends thereof, said at least one thermoplastic polymer being comprised in the thermoplastic elastomer vulcanizate according to a weight fraction ranging from 20% to 80%; - a second phase based on at least one two-component (B1 and B2) liquid silicone elastomer crosslinked by hydrosilylation which comprises a first component comprising a mixture of diorganopolysiloxanes, a reinforcing silica and a platinum-based hydrosilylation catalyst, and a second component comprising a diorganopolysiloxane, an organohydridosilicone compound, a reinforcing silica and an inhibitor, said at least one liquid silicone elastomer being comprised in the thermoplastic elastomer vulcanizate according to a weight fraction ranging from 20% to 80%; and - a system for compatibilizing these phases together, - at least one polymer chosen from the group consisting of grafted polyolefins, terpolymers containing poly(vinylaromatic/conjugated diene/methyl methacrylate) blocks, terpolymers containing poly(methyl methacrylate/alkyl acrylate/methyl methacrylate) blocks, ethylene/alkyl-(meth)acrylate/acrylic acid terpolymers and polymers resulting from at least one glycidyl ester such as ethylene/(meth)acrylate/glycidyl (meth)acrylate terpolymers; and - a polyorganosiloxane with SiH functional group(s), and in that said thermoplastic elastomer vulcanizate forms a homogeneous dispersion of said first and second phases obtained by reactive extrusion with at least the second phase which is continuous therein, said first phase being a discontinuous phase formed of nodules dispersed in said continuous second phase, or else the first and second phases being co-continuous in said thermoplastic elastomer vulcanizate in the form of nodules of one contained in the other and vice versa, these nodules having, in both cases, a mean size of less than 10 μm.