When using the standard definition of the term, The Holy Roman, Kaiserreich and Nazi states were certainly reichs: however, the phrase 'three reichs' refers to something more than simply three empires. Specifically, it refers to the three empires of German history.
Three Reichs of German History?
The history of modern German is often summarised as being 'three reichs and three democracies'. This is broadly correct, as modern Germany did indeed evolve out of a series of three empires - as described on the previous page - interspersed with forms of democracy; however, this does not automatically make the institutions German. While 'The First Reich' is a useful name for historians and students, applying it to the Holy Roman Empire is largely anachronistic. The imperial title and office of the Holy Roman Emperor drew, originally and in part, on the traditions of the Roman Empire, considering itself as an inheritor, not as the 'first'.
Indeed, it is highly debatable at what point, if ever, the Holy Roman Empire became a German body. Despite a near continuous core of land in northern central Europe, with a growing national identity, the reich extended into many of the modern surrounding territories, contained a mix of peoples, and was dominated for centuries by a dynasty of emperors commonly associated with Austria. To consider the Holy Roman Empire as solely German, rather than an institution within which there was a considerable German element, might be to lose some of this reich's character, nature and importance. Conversely, the Kaiserreich was a German state - with an evolving German identity - that partly defined itself in relation to the Holy Roman Empire. The Nazi Reich was also built around one particular concept of being 'German'; indeed, this latter reich certainly considered itself a descendant of the Holy Roman and German Empires, taking the title 'third', to follow them.
Three Different Reichs
The summaries given on the previous page may be very brief, but they are enough to show how these three empires were very different types of state; the temptation for historians has been to try and find some sort of linked progression from one to another. Comparisons between the Holy Roman Empire and the Kaiserreich began before this latter state was even formed. Historians and politicians of the mid 19th century theorised an ideal state, the Machtstaat, a "centralized, authoritarian and militarized power state" (Wilson, The Holy Roman Empire, Macmillan, 1999) this was, in part, a reaction to what they considered weaknesses in the old, fragmented, Empire. The Prussian led unification was welcomed by some as the creation of this Machtstaat, a strong German Empire which focused around a new emperor, the Kaiser. However, some historians began to project this unification back into both the 18th century and the Holy Roman Empire, 'finding' a long history of Prussian intervention when 'Germans' were threatened. Different again were the actions of some scholars in the aftermath of the Second World War, when attempts to understand how the conflict occurred led to the three reichs being seen as an inevitable progression through increasingly authoritarian and militarised governments.
An understanding of the nature, and relationship, of these three reichs is necessary for more than historical study. Despite a claim in the Chambers Dictionary of World History that "The term [Reich] is no longer used" (Dictionary of World History, ed. Lenman and Anderson, Chambers, 1993), politicians and others are fond of describing modern Germany, and even the European union, as a fourth Reich. They almost always use the term negatively, looking to the Nazi's and the Kaiser rather then the Holy Roman Empire, which might be a far better analogy for the current EU. Clearly, there is room for many differing opinions on the three 'German' reichs, and historical parallels are still being drawn with this term today.