Cursors And Concurrency

In a previous post, the theme of cursors and concurrency was touched as a secondary subject. I have a specific question about it as the primary one:

if we have
--------
create proc myProc
as
declare cursor for
select * from mytable
go
----------
if two or more clients(webpages for example)
execute myProc concurrently will the cursor be safe ? or would I have to make special arrangements, there are a couple of procs (that use cursors)that somebody else did and would not like to modify but we want to make the procs web available,

thank you