We study the notion of expansivity for both homeomorphisms and measures on 2-metric spaces [8]. At first glance we show that there are infinite compact continuous 2-metric spaces exhibiting expansive homeomorphisms in the 2-metric sense (roughly speaking 2-metric expansive homeomorphisms). Next we prove the absence of expansive measures in the 2-metric sense (or 2-metric expansive measures) for homeomorphisms of Sk (k = 1,2) equipped with the standard triangle-area A induced by Rk+1. We then conclude that there are no 2-metric expansive homeomorphisms of (Sk,A) for k = 1,2. Finally, it is proved that the set of the set of heteroclinic points for 2-metric expansive homeomorphisms on compact continuous 2-metric spaces is countable. This extends a well-known result by Reddy [19].