A learning algorithm of the fuzzy counterpropagation （FCP） neural network consists of two parts:updating the weight vectors from the input layer to the competitive layer

and the weight vectors from the competitive layer to the output layer.To use the clustering method and the gradient method to respectively update the former vectors

two learning algorithms of FCP network are proposed.The properties of the algorithms are analyzed

and some important theories are achieved.Finally

to apply the algorithms to a time series prediction problem based on the Mackey Glass equation

the experimental results show that the latter algorithm outperforms the former algorithm in learning precision and generalization ability

but learning speed of the former algorithm is faster than of the latter algorithm.