He played Gaelic football with his local club Castleisland Desmonds and at senior level for the Kerry county team between 1974 and 1991.
Nelli first came to prominence on the inter-county scene in the 1970s as goalkeeper on the Kerry minor football team.
In 1976 Nelligan made it two Munster under-21 titles in-a-row as Kerry retained their provincial crown at the expense of Cork.
In 1978 Nelligan made it four-in-a-row in Munster as Kerry retained their under-21 provincial crown at the expense of Cork again.
He came on as a substitute as both sides were hoping for success; however, new 'Dub' Kevin Moran was causing havoc with the Kerry defence.
[7] Two years later in 1978 Nelligan became the first-choice goalkeeper as Kerry faced little competition in the provincial championship once again.
The Kerry forward lobbed the ball over the head of Paddy Cullen, who was caught off his line arguing with the referee.
[9] In 1979 Kerry made it five-in-a-row in Munster as Cork fell by ten points in the provincial final.
Ger Power did not start the game, while John O'Keeffe got injured and Páidí Ó Sé was sent off during the encounter.
Another defeat of Cork in the provincial final gave Nelligan a third Munster winners' medal in succession.
The Connacht champions shocked Kerry and took a five-point lead inside the first twelve minutes.
Mikey Sheehy popped up again to score the decisive goal, as Kerry went on to claim a 1–9 to 1–6 victory in a game that contained sixty-four frees.
In 1981 Nelligan won his fourth consecutive Munster title, before lining out in the All-Ireland final against Offaly.
Kerry had the upper hand for much of the game and were leading by two points with two minutes left to be played.
'The Kingdom' bounced back the following year with Nelligan winning his third National League medal and his sixth Munster title.
Jack O'Shea scored a key goal after eleven minutes and Kerry stormed to a nine-point lead at half-time.
A Peter Quinn goal gave the Ulster men a six-point lead in the second-half; however, the game was far from over.
Pat Spillane ran fifty yards up the field for a hand-passed goal to get Kerry back on track.
Kerry were subsequently defeated by eventual champions Down in the All-Ireland semi-final and Nelligan decided to retire from inter-county football.
Nelligan's side lost out again in 1980; however, in 1981 he won his first Railway Cup winners' medal as Connacht were accounted for.