The paper is devoted to a generalization of the block Lanczos algorithm for a symmetric matrix, which allows the block size to be increased during the iterative process. In particular, the algorithm can be implemented with the block size chosen adaptively according to the clustering of Ritz values. The author considers an approach that is based on a single run of the algorithm. The adaptive algorithm, which is proposed, tests the clustering of Ritz values at each step and increases the block size when it is found inadequate. In this way all multiple and clustered eigenvalues can be found and the difficulty of choosing the block size is eased. Residual bounds for clustered eigenvalues are given. Numerical examples illustrate the adaptive algorithm.