In (Golchin A. and Rezaei P., Subpullbacks and flatness properties of S-posets. Comm. Algebra. 37: 1995-2007 (2009)) study was initiated of flatness properties of right s-posets as over a pomonoid that can be described by surjectivity of corresponding to certain (sub)pullback diagrams and new properties such as ( ) and ( ) were discovered. In this article first of all we describe poflatness properties of -posets over pomonoids by po-surjectivity of corresponding to certain subpullback diagrams. Then we introduce three new Conditions ( ), ( ) and ( ) and investigate the relation between them and Conditions ( ), ( ), ( ), ( ) , ( ) and ( ) . Also we describe these properties by po-surjectivity of corresponding to certain subpullback diagrams and describe Conditions ( ), ( ) and ( ) by weak po-surjectivity of corresponding to certain subpullback diagrams.