For analytic functions f(z) in the open unit disk U, there are many sufficient conditions for f (z) to be starlike and convex in U. In view of the paper by P.T. Mocanu [P.T. Mocanu, Some starlikeness conditions for analytic functions, Rev. Roumaine Math. Pures Appl. 33 (1988) 117-124], some extensions of sufficient conditions for f(z) to be starlike of order alpha and to be convex of order alpha are discussed. (C) 2011 Elsevier Ltd. All rights reserved.