This paper presents a row-action maximum likelihood algorithm (RAMLA), in which the relaxation parameter is controlled in such a way that the noise propagation from projection data to the reconstructed image is substantially independent of the access order of the input data (subsets) in each cycle of the sub-iterations. The 'subset-dependent' relaxation parameter lambda(k) (q) is expressed as lambda(k)(q) = beta0/(beta0 + q + gamma k M), where M is the number of angular views, q (0 < or = q < or = M - 1) is the access order of the angular view, k is the iteration number and beta0 and gamma are constants. The constant beta0 deals with the balance of the noise propagation and the constant gamma controls the convergence of iterations. The value of beta0 is determined from the geometrical correlation coefficients among lines of coincidence response. The proposed RAMLA using the subset-dependent (dynamic) relaxation 'dynamic RAMLA (DRAMA)' provides a reasonable signal-to-noise ratio with a satisfactory spatial resolution by a few iterations in the two-dimensional image reconstruction for PET. Dynamic OS-EM (DOSEM) has also been developed, which allows the use of a larger number of subsets (OS level) Msub without loss of signal-to-noise ratio as compared to the conventional OS-EM. DRAMA is a special case of DOSEM, where Msub = M, and it is no more profitable to use DOSEM with a smaller Msub (< M), because DRAMA provides similar performance with the fastest convergence and smallest computer burden. This paper describes the theory, algorithm and the results of the simulation studies on the performance of DRAMA and DOSEM.