The asymmetric geometry of polymeric nanonozzles provides two different transport directions: a converging direction (from the large opening to the small opening) and a diverging direction (from the small opening to the large opening). Asymmetric transport was observed in such nanochannels for both rigid polystyrene nanoparticles and flexible DNA molecules under a DC electric bias. Small, hard nanoparticles migrate easily in the diverging direction and tend to pack inside the nanochannel in the converging direction. In contrast, large, flexible DNA molecules transport better in the converging direction than in the diverging direction. A high electric field and a high velocity gradient along the tapered region produce different geometric constrictions and vortex-like particle motions for rigid nanoparticles, and also generate various coil-stretching dynamics for DNA molecules. Such nanonozzle arrays are useful in high flux and high sieving efficiency devices for biomolecule delivery or separation, and for loading trace amounts of drugs or genes for controlled drug and gene delivery.