The scaling behavior of cyclical surface growth (e.g., deposition/desorptio
n), with the number of cycles, n, is investigated. The roughness of surface
s grown by two linear primary processes follows a scaling behavior with asy
mptotic exponents inherited from the dominant process while the effective a
mplitudes are determined by both. Relevant nonlinear effects in the primary
processes may remain so or be rendered irrelevant. Numerical simulations f
or several pairs of generic primary processes confirm these conclusions. Ex
perimental results for the surface roughness during cyclical electrodeposit
ion/dissolution of silver show a power-law dependence on II, consistent wit
h the scaling description.