Kudla and Rapoport have defined a collection of special cycles on (integral models of) certain local Shimura varieties for unitary groups. They have showed up in the arithmetic fundamental lemma (AFL) conjecture arising from the relative trace formula approach to the arithmetic Gan-Gross-Prasad conjecture for the product unitary group U(n-1)xU(n). In this talk we will define some new special cycles (on local Shimura varieties) and use them to formulate new AFL conjectures.