This paper uses a multivariate extension of the non-parametric nonlinearity test from Hinich (1991) with the objective of investigating whether there is a nonlinear relation between the index of The Mexican Stock Exchange (IPC) and the peso/dollar exchange rate measured through the Cross-correlation and cross-correlation in the period 1994-2012 for three sub-periods of presidential administration. This method divides the sample into windows and provides information on nonlinear dependency. The main finding is that no significant cross-correlation windows are detected. However, time windows are observed with a significant cross bicorrelation, which suggests a non-linear and bidirectional relationship between the series. This paper concludes that for the three sub-periods of presidential administration both series maintain the same nonlinear and bidirectional relation for any change in the government with significant windows concentrated at the beginning of the presidential period regardless of the ruling party. Finally, It is important to note that the non-linear bidirectional periods were concentrated in the middle of the last Mexican presidential period, indicating that global external and economic financial factors affected this relationship. detectan ventanas de correlación cruzada significativas. No obstante se observan ventanas de tiempo con una bicorrelación cruzada significativa, lo que sugiere una relación no lineal y bidireccional entre las series. Este trabajo concluye que para los tres subperíodos de administración presidencial ambas series mantienen la misma relación no lineal y bidireccional para cualquier cambio en el gobierno con ventanas significativas concentradas al principio del período presidencial sin importar el partido gobernante. Porúltimo es importante destacar que los períodos no lineales bidireccionales se concentraron a mediados delúltimo período presidencial mexicano, lo que indica que los factores financieros externos y económicos globales afectaron esta relación.