Thanks very much: your suggestion worked perfectly, and I can create complex Property.
In addition to the 2 options, discussed up to now ...
... following Ricordisamoa's suggestion, I can create new COMPLEX Property via "API wrapping", also containing Statements with Qualifier and Reference!
import json ; import pywikibot ; site = pywikibot.Site('en', 'mywiki') ; site.login()
data = {u'aliases': {},
u'claims': {u'P2': [{u'mainsnak': {u'datatype': u'string',
u'datavalue': {u'type': u'string', u'value': u'value for test property'},
u'property': u'P2',
u'snaktype': u'value'},
u'qualifiers': {u'P3': [{u'datatype': u'string',
u'datavalue': {u'type': u'string',
u'value': u'string target for Qualifier'},
u'property': u'P3',
u'snaktype': u'value'}]},
u'qualifiers-order': [u'P3'],
u'rank': u'normal',
u'references': [{u'snaks': {u'P36': [{u'datatype': u'string',
u'datavalue': {u'type': u'string',
u'value': u'srting target for Reference'},
u'property': u'P36',
u'snaktype': u'value'}]},
u'snaks-order': [u'P36']}],
u'type': u'statement'}]},
u'datatype': u'string',
u'descriptions': {u'en': {u'language': u'en',
u'value': u'invented description'}},
u'labels': {u'en': {u'language': u'en',
u'value': u'Complex property created via API'}},
u'type': u'property'}
> Date: Fri, 25 Mar 2016 20:18:52 +0100
> Subject: Re: [pywikibot] How to create a new Property via pywikibot?
> Content-Type: text/plain; charset="utf-8"; Format="flowed"
>
> Example
>
> import json
> import pywikibot
>
> site = pywikibot.Site('en', 'mywiki')
> site.login()
> data = {
> 'datatype': 'string', # mandatory
> 'descriptions': {
> 'en': {
> 'language': 'en',
> 'value': 'invented description'
> }
> },
> 'labels': {
> 'en': {
> 'language': 'en',
> 'value': 'test property'
> }
> }
> }
> params = {
> 'action': 'wbeditentity',
> 'new': 'property',
> 'data': json.dumps(data),
> 'summary': 'my edit summary',
> 'token': site.tokens['edit']
> }
> req = site._simple_request(**params)
> print(req.submit())