The coorelation between vectors in a sequence of analysis frames are supposed to be specific to phonetic units in acoustic-phonetic decoding of speech. We propose non-linear vector interpolation techniques to represent this correlation and to recognize phonemes. The interpolation is based on the decomposition of a frame sequence into two parts and on the construction of a function that interpolates one part using information from the second part. According to quantities to be interpolated, three families of interpolator models are developed. In a recognition system, each phonetic symbol is associated with a non-linear vector interpolator which is trained to give minimum interpolation error for that specific phoneme. Multi-layer feedforward neural networks are used to implement the non-linear vector interpolators. For a continuous speech phoneme spotting test using 16 LPCC-derived cepstrum coefficients as parametric vectors, the three categories of models gave compatible results. Vector-pair interpolator models yielded best recognition rate. Compared to a VQ-coded reference technique, this model gives close global recognition rate and significatly outperforms for plosive sounds.