A notion of "delta-genus" for ample vector bundles $\mathcal{E}$ of rank two on a smooth projective threefold X is defined as a couple of integers (δ1, δ2). This extends the classical definition holding for ample line bundles. Then pairs (X, $\mathcal{E}$) with low δ1 and δ2 are classified under suitable additional assumptions on $\mathcal{E}$.
