It's important to realize that throughout the summer of 1918 the Bolsheviks were very preoccupied with ridding themselves of their political opponents, that is, first banning them from politics and then outright arresting them. According to Solzhenitsyn, the arrests of Mensheviks and Socialist Revolutionaries began immediately after June 14, 1918, after these parties had been officially "excluded from all the soviets [self-governing bodies]." The first arrests of the far-leftist Socialist Revolutionaries began from July 6. The point is, even before the murder of NAOTMAA, the Bolsheviks were eliminating the political opposition, and they obviously started with those who were most vulnerable. The terror itself began soon after, but I don't know when precisely people began massacring the "aristocracy." Actually I tend to think these were local actions, for the most part, and not directed from above. The Bolsheviks had much bigger fish to fry, perhaps starting with the IF.
Elisabeth, well stated. It's important to realise the"aristocracy" included hundreds or more in Russia at that time, not just the higher Romanovs and IF. Understood that way , and with Bolsheviks understood to mean more than just the most powerful figures in the Party, then the killing of the aristocracy happened relatively soon after the Bolshevik seizure of power. This was not in any organised way, because Bolshevik control wasn't completely secure, but random killings of vulnerable or "available" or particularly disliked aristocrats did start occurring as early as 1918. And the aristocracy was indeed vulnerable even immediately after the February revolution, though not solely to the Bolsheviks of course.
Thanks, Rodney! I do think it's a difficult question, for all kinds of reasons -- for one thing, what do we mean by the term "aristocracy"? As you say, the actual aristocracy in imperial Russia, as in Great Britain at this time, was extremely limited in number, probably only in the hundreds but definitely not in the thousands. The gentry, on the other hand, was a relatively much larger (and much poorer) group and I think suffered all the depredations of the revolution(s) of 1917, perhaps considerably more so than the actual aristocracy did -- if for no other reason than I think that members of the Russian gentry could not always afford a ticket out of the country, including all the bribes necessary to secure a safe passage.
Among the aristocracy I would certainly count such families as the Yusupovs, the Sheremetevs, the Bariatinskys, and the Golitsyns. Among the gentry -- landowning or not, because many of them had lost too much after the emancipation of the serfs in 1861 to really hold on to much if any land (a roughly similar situation to that of numerous members of the French nobility on the eve of the French Revolution) -- I would count the Nabokovs, who were only minor landowners in 1917. For all that, the father of the great novelist Vladimir Nabokov of
Lolita fame was a major political figure in the liberal movement in Russia before the revolution and was actually assassinated abroad, in emigration, after it, apparently by Russian monarchists. I suppose this fact alone (aside from his tremendous intellect) would account for Vladimir Nabokov's famous disdain, if not outright contempt for, both Russian communists and royalists.
But getting back to the point, I don't know enough about the aristocracy/gentry during the Civil War period to state with any certainty that the Bolsheviks began carrying out such and such murderous actions against the upper classes in such and such years. As far as my (limited) knowledge goes, most gentry and the few remaining actual aristocrats (members of the imperial family don't count, they were imperial, technically far, far above the aristocrats because they had "blue, blue blood") were arrested in successive waves by Lenin's regime beginning in the very early 1920s, and sent to concentration camps in Siberia and elsewhere. It's certainly true, however, that many people, not only of the upper classes, met violent deaths in these camps long before Stalin.
It's also true that there were many, according to the anecdotal evidence probably dozens, if not hundreds, of murders of nobles that took place during the great overall conflagration of the revolutionary year of 1917. But as I said before, I think these were mainly local, random actions, carried out by disgruntled peasants who were hungry for land and/or giving the hated landlords their ultimate payback.