  We prove existence of a special class of solutions to the (elliptic)
Nonlinear Schroeodinger Equation $- \epsilon^2 \Delta \psi + V(x) \psi =
|\psi|^{p-1} \psi$, on a manifold or in the Euclidean space. Here V represents
the potential, p an exponent greater than 1 and $\epsilon$ a small parameter
corresponding to the Planck constant. As $\epsilon$ tends to zero (namely in
the semiclassical limit) we prove existence of complex-valued solutions which
concentrate along closed curves, and whose phase is highly oscillatory.
Physically, these solutions carry quantum-mechanical momentum along the limit
curves. In this first part we provide the characterization of the limit set,
with natural stationarity and non-degeneracy conditions. We then construct an
approximate solution up to order $\epsilon^2$, showing that these conditions
appear naturally in a Taylor expansion of the equation in powers of $\epsilon$.
Based on these, an existence result will be proved in the second part.
