Recently, researchers at the Naval Research Laboratory have developed the SWORrD system for measuring two-dimensional Raman Spectra. The device consists of a tunable 2d ultraviolet laser that illuminates the sample at various wavelengths (210-300 nm) and collects a single Raman spectrum at each laser wavelength. The single spectra are combined to form a two-dimensional spectrum (laser wavelength by scattered wavenumber). In this paper we introduce a novel method for the detection of known agents (targets) within measured 2d spectra. Our method is bases on 'linear mixed pixel' techniques from hyperspectral imagery; in particular, we generalize the Adaptive Subspace Detector (ASD) to a form suitable for SWORrD samples. Our detector uses the individual laser runs to define a set of points within wavenumber space; the set of points corresponding to a 2d spectra defines a particular subspace that contains each material. These subspaces are then used with ASD to identify targets. We include experimental results using real-world data to illustrate our results.