This paper presents a generalized i-vector framework with phonetic tokenizations and tandem features for speaker verification as well as language identification. First, the tokens for calculating the zero-order statistics is extended from the MFCC trained Gaussian Mixture Models (GMM) components to phonetic phonemes, 3-grams and tandem feature trained GMM components using phoneme posterior probabilities. Second, given the calculated zero-order statistics (posterior probabilities on tokens), the feature used to calculate the first-order statistics is also extended from MFCC to tandem features and is not necessarily the same feature employed by the tokenizer. Third, the zero-order and first-order statistics vectors are then concatenated and represented by the simplified supervised i-vector approach followed by the standard back end modeling methods. We study different system setups with different tokens and features. Finally, selected effective systems are fused at the score level to further improve the performance. Experimental results are reported on the NIST SRE 2010 common condition 5 female part task and the NIST LRE 2007 closed set 30 seconds task for speaker verification and language identification, respectively. The proposed generalized i-vector framework outperforms the i-vector baseline by relatively 45% in terms of equal error rate (EER) and norm minDCF values.