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Several speech synthesis and voice conversion techniques can easily generate or manipulate speech to deceive the speaker verification (SV) systems. Hence, there is a need to develop spoofing countermeasures to detect the human speech from spoofed speech. System-based features have been known to contribute significantly to this task. In this paper, we extend a recent study of Linear Prediction (LP) and Long-Term Prediction (LTP)-based features to LP and Nonlinear Prediction (NLP)-based features. To evaluate the effectiveness of the proposed countermeasure, we use the corpora provided at the ASVspoof 2015 challenge. A Gaussian Mixture Model (GMM)-based classifier is used and the % Equal Error Rate (EER) is used as a performance measure. On the development set, it is found that LP-LTP and LP-NLP features gave an average EER of 4.78% and 9.18%, respectively. Score-level fusion of LP-LTP (and LP-NLP) with Mel Frequency Cepstral Coefficients (MFCC) gave an EER of 0.8% (and 1.37%), respectively. After score-level fusion of LP-LTP, LP-NLP and MFCC features, the EER is significantly reduced to 0.57%. The LP-LTP and LP-NLP features have found to work well even for Blizzard Challenge 2012 speech database.