Ramsey numbers similar to those of van der Waerden are examined. Rather than considering arithmetic sequences, we look at increasing sequences of positive integers { x 1, x 2,…, x n } for which there exists a polynomial ⨍(x)=∑ r i =0a ix i , with a i ϵZ and x j +1=⨍(x j) . We denote by p r ( n) the least positive integer such that if [1,2,…, p r ( n)] is 2-colored, then there exists a monochromatic sequence of length n generated by a polynomial of degree ⩽ r. We give values for p r ( n) for n⩽5, as well as lower bounds for p 1( n) and p 2( n). We also give an upper bound for certain Ramsey numbers that are in between p n −2( n) and the nth van der Waerden number.