A random-phase approximation (RPA) treatment of edge magnetoplasmons (EMP) ispresented for strong magnetic fields, low temperatures, and integer fillingfactors \nu. It is valid for negligible dissipation and lateral confiningpotentials smooth on the scale of the magnetic length \ell_{0} but sufficientlysteep that the Landau-level (LL) flattening can be neglected. LL coupling,screening by edge states, and nonlocal contributions to the current density aretaken into account. In addition to the fundamental mode with typical dispersionrelation \omega\sim q_x \ln(q_{x}), fundamental modes with {\it acoustic}dispersion relation \omega\sim q_x are obtained for \nu>2. For \nu=1,2 a {\bfdipole} mode exists, with dispersion relation \omega\sim q_x^3, that isdirectly related to nonlocal responses.
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