In recent years, due to the Indian Federal Government's and Tamil Nadu State Government's various initiatives and promotional activities, foreign and domestic tourist arrivals in Tamil Nadu are on the increase. This article aims to model the monthly tourist arrivals (foreign as well as domestic) in Tamil Nadu for monthly time series data during the period 1998 to 2002 using univariate time-series models. As both time series show strong seasonal patterns, we also investigate the possibility of seasonal unit roots in the domestic and foreign tourist arrivals series. The results show that significant growth in domestic and foreign arrivals takes place during the months December to January. Growth rate for domestic tourist arrivals is positive during April and May, but is negative for the foreign tourist arrivals during April and insignificant during May. Such information would be very useful to the Tamil Nadu government and the tourism industry in maximizing the usage of available tourist spot infrastructure and to provide high quality service.