  In this paper, a de Casteljau algorithm to compute (p,q)-Bernstein Bezier
curves based on (p,q)-integers is introduced. We study the nature of degree
elevation and degree reduction for (p,q)-Bezier Bernstein functions. The new
curves have some properties similar to q-Bezier curves. Moreover, we construct
the corresponding tensor product surfaces over the rectangular domain (u, v)
\in [0, 1] \times [0, 1] depending on four parameters. We also study the de
Casteljau algorithm and degree evaluation properties of the surfaces for these
generalization over the rectangular domain. Furthermore, some fundamental
properties for (p,q)-Bernstein Bezier curves are discussed. We get q-Bezier
curves and surfaces for (u, v) \in [0, 1] \times [0, 1] when we set the
parameter p1 = p2 = 1.
