Dynamic threshold neural P systems (DTNP systems, for short) are a kind of distributed parallel computing systems abstracted from the spiking and dynamic threshold mechanisms of neurons. A DTNP system consists of several dynamic threshold neurons, and each neuron has a data unit and a threshold unit. The computational completeness of DTNP systems has been investigated. DTNP systems are synchronous systems, and a global clock is assumed to synchronize all threshold neurons. However, the assumption is biologically non-realistic. In this paper, we discuss DTNP systems working in sequential mode, i.e., sequential DTNP systems (SDTNP systems, in short). Based on the number of spikes of active neurons and the ruleapplication strategy, four sequentiality strategies are considered. It is proven that SDTP systems working in four sequentiality strategies are Turing universal number generating/accepting devices.