A semiconductor wafer processing tape includes a permanent backing and a layer of a nonpressure sensitive adhesive. The tapes are useful for wafer grinding and/or wafer dicing applications. The nonpressure sensitive adhesive includes a copolymer of at least one of a first monoethylenically unsaturated monomer, at least one of a second monoethylenically unsaturated monomer, and at least one copolymerizable nonionic crosslinking agent; wherein the second monoethylenically unsaturated monomer is a reinforcing monomer having a homopolymer glass transition temperature higher than that of the first monoethylenically unsaturated monomer. A method of processing semiconductor wafers is also provided.