We consider the random sequential adsorption (RSA) of line segments with diffusional relaxation on a one-dimensional lattice by using Monte Carlo method. The line segments with a length k deposit with a probability p or diffuse up to a diffusion length l(l less than or equal to k) with a probability 1 - p. We observe a power-law behavior of the coverage fraction theta(t). For the dimer k = 2, the empty area fraction decays according to 1 - theta(t) = 5(l) p(0.68)(1 - p)(-0.40)(pt)(-0.5), regardless of the diffusion length and the adsorption probability. The dynamics of empty area fraction of the dimers is equivalent to the diffusion-limited reaction (DLR), A + A --> 0, at the long time limits. A single empty site at the RSA corresponds to the reactants A at the DLR. For k greater than or equal to 4, the empty area fraction decays according to the power law as 1 - theta(t) = A(k, l)[(1 - p)pt](-a(k,l)). For k greater than or equal to 4, the dynamics of empty area fraction is not interpreted by the kinetics of the diffusion-limited reaction, kA --> 0. For k greater than or equal to 3, the model with l > 1 stepping corresponds to reactions where the particles (gaps of size l) hop in a correlated way. Thus, our model of l-group-diffusion-limited k-particle reactions is different from those of the ordinary reaction kA --> 0. We found new power law behavior for l-group-diffusion limited k-particle reactions and the exponents of the power law depend on the hopping length l. We observed a mixed dynamics of the gap creations, splitting, and annihilations for the model at the long time. (C) 2003 American Institute of Physics.