  The dynamic surface critical behavior of macroscopic systems whose dynamic
bulk critical behavior is described by model $B$ is investigated. The
semi-infinite extensions of bulk model $B$ introduced in a previous treatment
[Phys. Rev. B 49, 2846 (1994)] and called models $B_A$ and $B_B$ are studied in
detail by means of field-theoretic RG methods. The distinctive feature of these
models is the presence or absence of relevant nonconservative surface terms.
The earlier results on the structure of the required counterterms, the flow
equations, and the representation of the surface critical exponents of dynamic
quantities at the ordinary and special phase transitions in terms of static
bulk and surface exponents are corroborated by means of an explicit two-loop
calculation for $4-\epsilon$ dimensions. For parameter values corresponding to
a given static surface universality class, models $B_A$ and $B_B$ represent
distinct dynamic surface universality classes. Differences between these
manifest themselves in the behavior of scaling functions for dynamic surface
susceptibilities. RG-improved perturbation theory is used to compute some of
these susceptibilities to one-loop order.
