Describes doing things sequentially, each in its proper turn, often with a sense of methodical progression.
Our names were called one by one.
Let's solve the problems one after another.
The teacher handed out the worksheets to the students one by one.
The receptionist called out names in turn and guided each person.
The children lined up in turn and boarded the bus.
I will explain the steps one by one.
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.
一斉に means 'all at once, simultaneously', the opposite of 順々に's step-by-step, one-at-a-time progression.
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.
Standard kanji spelling with iteration mark; the most common written form.
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.