In the context of detection of weeds in crops for site-specific weed control, on-ground spectral reflectance measurements are the first step to determine the potential of remote spectral data to classify weeds and crops. Field studies were conducted for four years at different locations in Spain. We aimed to distinguish cruciferous weeds in wheat and broad bean crops, using hyperspectral and multispectral readings in the visible and near-infrared spectrum. To identify differences in reflectance between cruciferous weeds, we applied three classification methods: stepwise discriminant (STEPDISC) analysis and two neural networks, specifically, multilayer perceptron (MLP) and radial basis function (RBF). Hyperspectral and multispectral signatures of cruciferous weeds, and wheat and broad bean crops can be classified using STEPDISC analysis, and MLP and RBF neural networks with different success, being the MLP model the most accurate with 100%, or higher than 98.1%, of classification performance for all the years. Classification accuracy from hyperspectral signatures was similar to that from multispectral and spectral indices, suggesting that little advantage would be obtained by using more expensive airborne hyperspectral imagery. Therefore, for next investigations, we recommend using multispectral remote imagery to explore whether they can potentially discriminate these weeds and crops.