MSC: 47H09 47H10 47H30 Keywords: Weak topology Measure of weak noncompactness Fixed point theorem Nonlinear alternative Hammerstein equation This paper is devoted to establishing new variants of some nonlinear alternatives of Leray-Schauder and Krasnosel'skij type involving the weak topology of Banach spaces. The De Blasi measure of weak noncompactness is used. An application to solving a nonlinear Hammerstein integral equation in L 1 spaces is given. Our results complement recent ones in [K. Latrach, M.A. Taoudi, A. Zeghal, Some fixed point theorems of the Schauder and the Krasnosel'skij type and application to nonlinear transport equations, J. Differential Equations 221 (2006) 256-2710] and [K. Latrach, M.A. Taoudi, Existence results for a generalized nonlinear Hammerstein equation on L 1 spaces, Nonlinear Anal. 66 (2007) 2325-2333].