  We study the x- and y-regularity of a bigraded K-algebra R. These notions are
used to study asymptotic properties of certain finitely generated bigraded
modules. As an application we get for any equigenerated graded ideal I upper
bounds for the number j_0 for which reg(I^j) is a linear function for j >= j_0.
Finally we give upper bounds for the x- and y-regularity of generalized
Veronese algebras.
