Summary: Observations have been made of closed systems of nutrient and phytoplankton in the Biology Department at the Universiti Brunei Darussalam. The population of phytoplankton grew to a maximum and then declined with some evidence of a continuing small amplitude oscillation. A simple time delay differential equation model is used to describe the behaviour. A combination of analytical and numerical methods is used to examine the behaviour of this model, in particular the occurrence of steady states and limit cycles and consideration of their stability.