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Sequential transitions between metastable states are ubiquitously observed in the neural system and underlie various cognitive functions. Although a number of studies with asymmetric Hebbian connectivity have investigated how such sequences are generated, the focused sequences are simple Markov ones. On the other hand, supervised machine learning methods can generate complex non-Markov sequences, but these sequences are vulnerable against perturbations. Further, concatenation of newly learned sequence to the already learned one is difficult due to catastrophe forgetting, although concatenation is essential for cognitive functions such as inference. How stable complex sequences are generated still remains unclear. We have developed a neural network with fast and slow dynamics, which are inspired by the experiments. The slow dynamics store history of inputs and outputs and affect the fast dynamics depending on the stored history. We show the learning rule that requires only local information can form the network generating the complex and robust sequences in the fast dynamics. The slow dynamics work as bifurcation parameters for the fast one, wherein they stabilize the next pattern of the sequence before the current pattern is destabilized. This co-existence period leads to the stable transition between the current and the next pattern in the sequence. We further find that timescale balance is critical to this period. Our study provides a novel mechanism generating the robust complex sequences with multiple timescales in neural dynamics. Considering the multiple timescales are widely observed, the mechanism advances our understanding of temporal processing in the neural system.