We consider wavelet decompositions of Haar type spaces on arbitrary nonuniform grids by methods of the nonclassical theory of wavelets. The number of nodes of the original (nonuniform) grid can be arbitrary, and the main grid can be any subset of the original one. We proposie decomposition algorithms that take into account the character of changes in the original numerical flow. The number of arithmetical operations is proportional to the length of the original flow, and successive real-time processing is possible for the original flow. We propose simple decomposition and reconstruction algorithms leading to formulas where the coefficients are independent of the grid and are equal to 1 in absolute value.