The paper deals with the existence of positive multipeak solutions of the semilinear Neumann problem \[ -\varepsilon^2 \Delta u+u= u^p\quad \text{in}\;\Omega,\qquad \partial u/\partial\nu=0\quad \text{on}\;\partial\Omega, \] where \(\Omega\subset\mathbb R^N\) is a bounded and smooth domain, \(N\geq 2,\) \(\varepsilon >0,\) \(11\) if \(N=2,\) and \(\nu\) is the unit outward normal to \(\partial\Omega.\)