Gliomas are the most frequent primary brain tumours. During neurosurgical treatment, locating the exact tumour border is often difficult. This study assesses grading of astrocytomas based on Raman spectroscopy for a future application in intra-surgical guidance. Our predictive classification models distinguish the surgically relevant classes "normal tissue" and "low" and "high grade astrocytoma" in Raman maps of moist bulk samples (80 patients) acquired with a fibre-optic probe. We introduce partial class memberships as a strategy to utilize borderline cases for classification. Borderline cases supply the most valuable training and test data for our application. They are (a) examples of the sought boundary and (b) the cases for which new diagnostics are needed. Besides, the number of suitable training samples increases considerably: soft logistic regression (LR) utilizes 85% more spectra and 50% more patients than linear discriminant analysis (LDA). The predictive soft LR models achieve ca. 85, 67 and 84% (normal, low and high grade) sensitivity and specificity. We discuss the different heuristics of LR and LDA in the light of borderline samples. While we focus on prediction, the spectroscopic interpretation of the predictive models agrees with previous descriptive studies. Unsaturated lipids are used to differentiate between normal and tumour tissues, while the total lipid content prominently contributes to the determination of the tumour grade. The high-wavenumber region above 2,800 cm^-1 alone did not allow successful grading. We give a proof of concept for Raman spectroscopic grading of moist astrocytoma tissues and propose to include borderline samples into classifier training and testing.