Which is grammatical?
- response time of multiple services
- response times of multiple services
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Response time would be appropriate if you wanted to refer to the response time of all the services as a whole. For example:
However, if you want to refer to multiple time instances or a time interval then use response times. For example:
It depends on the rest of the sentence.
A bit more context would be welcome. With what you posted I'd go with "response times"
"The response times of our intranet and extranet services have improved by 10% over the last month."
"The response time of our intranet and extranet services is perceived as slow by most users."
Both work. It depends on the context, IMO.