The Computational Grid is a promising platform for the deployment 
of high-performance computing applications.  A number of projects 
have addressed the idea of software as a service on the network. 
These systems usually implement client-server architectures
with many servers running on distributed Grid resources and have 
commonly been referred to as Network-enabled servers (NES). 
An important question is that of {\em scheduling} in this 
multi-client multi-server scenario. Note that in this context most
requests are computationally intensive as they are generated
by high-performance computing applications. 
The Bricks simulation framework has been developed and extensively 
used to evaluate scheduling strategies for NES systems. 
In this paper we discuss a deadline scheduling strategy that is 
appropriate for the multi-client multi-server case. 
We propose a simple deadline scheduling algorithm and then augment 
it with Load Correction and Fallback mechanisms which could improve 
the performance of the algorithm in our context. We then give 
simulation results and draw conclusion on the value and feasibility
of deadline scheduling for NES systems on the Grid.