  In this paper we obtain scaling limits of $\Lambda$-coalescents near time
zero under a regularly varying assumption. In particular this covers the case
of Kingman's coalescent and beta coalescents. The limiting processes are
coalescents with infinite mass, obtained geometrically as tangent cones of
Evans metric space associated with the coalescent. In the case of Kingman's
coalescent we are able to obtain a simple construction of the limiting space
using a two-sided Brownian motion.
