Although the offering of financial products and services over the Internet by banks and financial institutions continues to spread, reports on Internet banking show that the adoption and usage of such services by consumers are low. Further, relatively little empirical research has been carried out to examine factors influencing users' adoption or use of Internet banking services, particularly in New Zealand. Hence, there is a need to identify relevant factors that influence New Zealand's bank customers' intentions to use Internet banking. This research used two commonly applied and empirically supported models of information technology adoption to achieve this objective. In this study, Davis's (1989) technology acceptance model (TAM) is extended by two external variables, namely risk and self-efficacy. The second model used is a reduced version of Moore and Benbasat's (1991) perceived characteristics of innovation (PCI) model, without the image and voluntariness constructs. A questionnaire was used to conducting a postal survey of 1000 individuals in Auckland, New Zealand. Out of 163 responses received 157(15.7%) were usable and with this data both research models were tested.The results reveal that perceived usefulness, perceived ease of use, self-efficacy, relative advantage, compatibility, and result demonstrability have a significant association with intention to use Internet banking, while risk, visibility and trialability are not significant. Both the modified TAM and PCI models used in the study have a similar explanatory power of slightly over 20% of the variance in intention. In the TAM model, perceived usefulness and self-efficacy are significant variables, while compatibility is the only variable significant for the PCI model. Further, results indicate that users' perceptions of various aspects of Internet banking are more positive than non-users' perceptions, except for risk.The results of this study indicate that both TAM and PCI have low capabilities in explaining the variances in users' intention to adopt or use Internet banking services. Therefore, further studies are recommended to examine the performance of these models in Internet banking studies and also to improve the prediction power of these models by incorporating additional constructs. Although risk is found to be insignificant in this study, considering results of prior studies, further studies are required to examine its influence on intention.For banks point of view, banks should consider launching campaigns to demonstrate the usefulness and benefits. Once users perceive that advantages outweigh disadvantages, they are more likely to adopt or use Internet banking. Additionally, banks must make continuous effort to understand consumers' requirement and design and deliver their products and services in such a way that it is consistent with customers' requirements, beliefs and the way customers are accustomed to work. Banks website should facilitate customers with a 'one stop comprehensive financial' service. Banks can arrange hands-on training for prospective users to enhance their self-efficacy or may pay additional interest on online-deposit accounts (can be access through Internet only). Besides promoting services, banks need to invest in staff education and training and be equipped with advanced computer technology.