That is a very bad design pattern. The best design for web services is for them to be without state.
One design would be to combine both requests into one, which retrieves and processes the dataset.
If this is not practical, then you can use Session state.
In either case, you should be using WCF instead of the legacy ASMX web services. This is a technology which should not be used for new development.
John Saunders
WCF is Web Services. They are not two separate things.
Use WCF for All New Web Service Development, instead of legacy ASMX or obsolete WSE
Use File->New Project to create Web Service Projects