  A restricted dynamics, previously introduced in a kinetic model for
relaxation phenomena in linear polymer chains, is used to study the dynamic
critical exponent of one-dimensional Ising models. Both the alternating
isotopic chain and the alternating-bond chain are considered. In contrast with
what occurs for the Glauber dynamics, in these two models the dynamic critical
exponent turns out to be the same. The alternating isotopic chain with the
restricted dynamics is shown to lead to Nagel scaling for temperatures above
some critical value. Further support is given relating the Nagel scaling to the
existence of multiple (simultaneous) relaxation processes, the dynamics
apparently not playing the most important role in determining such scaling.
