Wiener systems identification is studied in the presence of possibly infinite-order linear dynamics and memory nonlinear operators of backlash and backlash-inverse types. The latter is laterally bordered with polynomial lines of arbitrary-shape. It turns out that the borders are allowed to be noninvertible and crossing making possible to account, within a unified theoretical framework, for memory and memoryless nonlinearities. Moreover, the prior knowledge of the nonlinearity type, being backlash or backlash-inverse or memoryless, is not required. Using sine excitations, and getting benefit from model plurality, the initial complex identification problem is made equivalent to two tractable (though still nonlinear) prediction-error problems. These are coped with using linear and nonlinear least squares estimators which all are shown to be consistent. (C) 2013 Elsevier Ltd. All rights reserved.