ā < PIE Ḥ (i.e. roots ending in a laryngeal, although widely extended to other roots). This class shows root ablaut, with original e-grade (and palatalization of the initial root consonant) in the active singular, contrasting with zero-grade (and no palatalization) elsewhere. II: This class has reduplication in Tocharian A (possibly reflecting the PIE reduplicated aorist). However, Tocharian B has a vowel reflecting long PIE ē, along with palatalization of the initial root consonant. There is no ablaut in this class. III: This class has a suffix s in the 3rd singular active and throughout the mediopassive, evidently reflecting the PIE sigmatic aorist. Root ablaut occurs between active and mediopassive. A few verbs have palatalization in the active along with s in the 3rd singular, but no palatalization and no s in the mediopassive, along with no root ablaut (the vowel reflects PToch ë). This suggests that, for these verbs in particular, the active originates in the PIE sigmatic aorist (with s suffix and ē vocalism) while the mediopassive stems from the PIE perfect (with o vocalism). IV: This class has suffix ṣṣā, with no ablaut. Most verbs in this class are causatives. V: This class has suffix ñ(ñ)ā, with no ablaut. Only a few verbs belong to this class. VI: This class, which has only two verbs, is derived from the PIE thematic aorist. As in Greek, this class has different endings from all the others, which partly reflect the PIE secondary endings (as expected for the thematic aorist). All except preterite class VI have a common set of endings that stem from the PIE perfect endings, although with significant innovations. Imperative The imperative likewise shows 6 classes, with a unique set of endings, found only in the second person, and a prefix beginning with p-. This prefix usually reflects Proto-Tocharian *pä- but unexpected connecting vowels occasionally occur, and the prefix combines with vowel-initial and glide-initial roots in unexpected ways. The prefix is often compared with the Slavic perfective prefix po-, although the phonology is difficult to explain. Classes i through v tend to co-occur with preterite classes I through V, although there are many exceptions. Class vi is not so much a coherent class as an "irregular" class with all verbs not fitting in other categories. The imperative classes tend to share the same suffix as the corresponding preterite (if any), but to have root vocalism that matches