順じゅん々じゅんに

Meanings

Describes doing things sequentially, each in its proper turn, often with a sense of methodical progression.

〈人ひと〉〉に順々じゅんじゅんに〈物もの〉〉を配くばるto hand things out to people one by one, in order
先せん生せいは生せい徒とに順じゅん々じゅんにプリントを配くばった。
The teacher handed out the worksheets to the students one by one.
順々じゅんじゅんに〈人ひと〉〉の名前なまえを呼よぶto call out people's names one by one, in turn
受うけ付つけは順じゅん々じゅんに名な前まえを呼よんで案あん内ないした。
The receptionist called out names in turn and guided each person.
順々じゅんじゅんに並ならぶto line up one after another, in order
子こ供どもたちは順じゅん々じゅんに並ならんでバスに乗のった。
The children lined up in turn and boarded the bus.
順々じゅんじゅんに〈事こと〉〉を説明せつめいするto explain things one by one, step by step
手て順じゅんを順じゅん々じゅんに説せつ明めいしていきます。
I will explain the steps one by one.

順じゅんに
順に is a general term for doing things in order, while 順々に emphasizes a step-by-step, sequential progression through each item.
順じゅん番ばんに
順番に and 順々に both mean 'in turn', but 順番に focuses on taking one's place in a queue or list, while 順々に stresses the methodical, step-by-step progression through each item.
次つぎ々つぎにN1
次々に means 'one after another' in rapid succession without implying a fixed order, whereas 順々に implies following a set, methodical sequence.

一いっ斉せいにN2
一斉に means 'all at once, simultaneously', the opposite of 順々に's step-by-step, one-at-a-time progression.

徐じょ々じょにN3
徐々に means 'gradually' (describing a slow change over time), while 順々に means 'in turn, one by one' through a sequence of items.

順じゅん々じゅんに
Standard kanji spelling with iteration mark; the most common written form.
順じゅん順じゅんに
Alternative spelling without the iteration mark; less common but still used.

Reduplication of 順 (order, turn) with the adverbial particle に, emphasizing a sequential, step-by-step manner.