The knowledge of the dependence pattern of daily weather variables, which tend to persist in time, is important in developing techniques for simulating weather data. The dependence of daily maximum and minimum temperatures is presented for 17 stations in the three main climatic zones (humid, sub-humid and semi-arid) of Nigeria. Daily maximum and minimum temperatures have an average lag-one serial correlation coefficient of 0.833 and 0.802, respectively, depending more on latitude followed by elevation of the site. The correlation between maximum and minimum temperature averaged 0.387 and also varied with season and location. The results of the Student's T-test show that persistence within maximum and minimum temperatures and interdependence between the two meteorological variables did not differ significantly, 95% of the times, at most of the sites. The implication of these in developing limited area models for weather forecasting and regional climate studies has been stressed.