adverb
gradually; little by little; step by step
Adverb usually followed by に. Describes a slow, incremental change or progression.
See also: 次第次第に
春が近づくにつれて、次第次第に暖かくなってきた。
As spring approaches, it has gradually become warmer.
彼は次第次第に自信をつけていった。
He gradually gained confidence.
次第に is the standard, more common adverb for 'gradually'. 次第次第に is a slightly more emphatic or literary variant.
徐々に also means 'gradually', but is more formal and often used in written or technical contexts.
Reduplication of 次第 (しだい), which originally meant 'order' or 'circumstances'. The repetition emphasizes a step-by-step progression.