This paper is concerned with the neutral dynamic equation
on a time scale T. An interval condition is imposed on the neutral delay term and on the nonneutral deviating argument term that allows to be locally nonincreasing. The term can be delay, advanced, or can oscillate about zero. The influence of oscillation of is addressed along with a positive number for both regular and nonregular oscillation with respect to . Results involve integrals of combinations of and as well as auxiliary functions. Applications to difference equations are given.