Two quantum nondemolition (QND) measurement schemes using second order optical nonlinearities are proposed and shown to fulfil hte criteria for back-action evasion in a measurement of optical amplitude. The first scheme, based on optical rectification, is very simple in principle, but yields extremely small signals with available materials. The second scheme is based on optical parametric amplication with type II phase matching. The interactions necessary for back-action evasion are provided by polarization mixing using Faraday rotation. © 1987.