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Dengue Fever is a dangerous viral disease that is transmitted by female Aedes mosquitoes and is common in more than 100 countries in the world and in all countries of South-East Asia. Mathematical models of Dengue Fever transmission are useful for studying the causes of the spread of the disease and to try to develop methods for reducing the spread of the disease. In this paper, a mathematical model for Dengue fever is analyzed consisting of a system of four nonlinear differential equations with two time delays. The model includes infected humans, infectious humans, infected mosquitoes and infectious mosquitoes. The model has disease-free and endemic equilibrium points. The asymptotic stability of the equilibrium points are studied analytically. The Matlab computer program is used to obtain numerical solutions of the model for both zero and nonzero time delays for a range of parameter values. It is found that for some reasonable estimates of parameter values the endemic equilibrium point is asymptotically stable, but the approach to equilibrium is very slow, suggesting that this equilibrium point may not be of practical importance for these parameter values. Some comparisons are made between the model results and the actual data for Dengue Fever in Thailand, Malaysia and Singapore. [ABSTRACT FROM AUTHOR]