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Mutually beneficial interactions between flowering plants and animal pollinators represent a critical 'ecosystem service' under threat of anthropogenic extinction. We explored probable patterns of extinction in two large networks of plants and flower visitors by simulating the removal of pollinators and consequent loss of the plants that depend upon them for reproduction. For each network, we removed pollinators at random, systematically from least-linked (most specialized) to most-linked (most generalized), and systematically from most- to least-linked. Plant species diversity declined most rapidly with preferential removal of the most-linked pollinators, but declines were no worse than linear. This relative tolerance to extinction derives from redundancy in pollinators per plant and from nested topology of the networks. Tolerance in pollination networks contrasts with catastrophic declines reported from standard food webs. The discrepancy may be a result of the method used: previous studies removed species from multiple trophic levels based only on their linkage, whereas our preferential removal of pollinators reflects their greater risk of extinction relative to that of plants. In both pollination networks, the most-linked pollinators were bumble-bees and some solitary bees. These animals should receive special attention in efforts to conserve temperate pollination systems.