Summary: A labding of a graph \(G(V,E)\) is an \((a,d)\)-vertex antimagic total labeling if it assigns the vertices and edges the consecutive integers from 1 to \(|V|+|E|\) with the property that the sums for each vertex of its label and the labels on its incident edges form an arithmetic progression with initial term \(a\) and common difference \(d\). We give some positive and negative results on the existence of vertex antimagic total labelings of paths and cycles.