This paper presents mathematical models for tuberculosis and its dynamics under the implementation of the direct observation therapy strategy (DOTS) in Nigeria. The models establish conditions for the eradication of tuberculosis in Nigeria based on the fraction of detected infectious individuals placed under DOTS for treatment. Both numerical and qualitative analysis of the models were carried out and the effect of the fraction of detected cases of active TB on the various epidemiological classes is investigated. The results showed that, provided that the fraction of detected infectious individuals exceeded a critical value, there exists a globally stable disease free equilibrium. However, if this critical detection level is not reached, the disease-free equilibrium will be unstable even with the very high probability successful treatment under DOTS. The results showed that DOTS expansion in Nigeria must include significant increase in the detection rate of infectious individuals; otherwise the effect in reducing the incidence in Nigeria will not be achieved disregarding the tremendous efforts in any other direction, and the huge number of undetected cases will make DOTS insignificant with respect to tuberculosis control.