In this article we continue the study of property N p of irrational ruled surfaces begun in [E. Park, On higher syzygies of ruled surfaces, math.AG/0401100, Trans. Amer. Math. Soc., in press]. Let X be a ruled surface over a curve of genus g ⩾ 1 with a minimal section C 0 and the numerical invariant e. When X is an elliptic ruled surface with e = − 1 , it is shown in [F.J. Gallego, B.P. Purnaprajna, Higher syzygies of elliptic ruled surfaces, J. Algebra 186 (1996) 626–659] that there is a smooth elliptic curve E ⊂ X such that E ≡ 2 C 0 − f . And we prove that if L ∈ Pic X is in the numerical class of a C 0 + b f and satisfies property N p , then ( C , L | C 0 ) and ( E , L | E ) satisfy property N p and hence a + b ⩾ 3 + p and a + 2 b ⩾ 3 + p . This gives a proof of the relevant part of Gallego–Purnaprajna' conjecture in [F.J. Gallego, B.P. Purnaprajna, Higher syzygies of elliptic ruled surfaces, J. Algebra 186 (1996) 626–659]. When g ⩾ 2 and e ⩾ 0 we prove some effective results about property N p . Let L ∈ Pic X be a line bundle in the numerical class of a C 0 + b f . Our main result is about the relation between higher syzygies of ( X , L ) and those of ( C , L C ) where L C is the restriction of L to C 0 . In particular, we show the followings: (1) If e ⩾ g − 2 and b − a e ⩾ 3 g − 2 , then L satisfies property N p if and only if b − a e ⩾ 2 g + 1 + p . (2) When C is a hyperelliptic curve of genus g ⩾ 2 , L is normally generated if and only if b − a e ⩾ 2 g + 1 and normally presented if and only if b − a e ⩾ 2 g + 2 . Also if e ⩾ g − 2 , then L satisfies property N p if and only if a ⩾ 1 and b − a e ⩾ 2 g + 1 + p .