You're probably using session_auto_start or something. Run session_write_close() as first statement to close the session, this will allow your script to run concurrently.

Thanks for the quick reply, but

I modified the sample script to
<?php 
session_write_close();
print ("starting1");
flush ();
touch ("foo.dat");
sleep (60);
?>
Done.

but it has no effect.  
The flush call is only for demonstration/debug, my actual
script where I noticed the problem doesn't have this call.
The
contents of php.ini Session section are (comments removed),
pretty standard I believe:
[Session]
session.save_handler      = files
session.save_path         = /tmp
session.use_cookies       = 1
session.name              = PHPSESSID
session.auto_start        = 0
session.cookie_lifetime   = 0                                    
session.cookie_domain     =         session.serialize_handler = php     
session.gc_probability    = 1                                    
session.gc_maxlifetime    = 1440
session.referer_check     =                                      
session.entropy_length    = 0 
session.entropy_file      =   
;  session.entropy_length    = 16
;  session.entropy_file      = /dev/urandom
session.cache_limiter     = nocache                                     
session.use_trans_sid     = 1 
url_rewriter.tags         =
"a=href,area=href,frame=src,input=src,form=fakeentry"

There is something more at work here, and
current evidense points away from php5.