PWC: When a capture is made, the captured unit (except a King) is replaced on the square the capturing unit just leaves. A Pawn is immovable on its 1st rank.

Madrasi: Units, other than Kings, are paralysed when they attack each other. Paralysed units cannot move, capture or give check, their only power being that of causing paralysis.
Madrasi RI (rex inclusive): the rule applies to Kings as well, so the two Kings may stand next to each other.

Alphabetic Chess: The squares are considered in the order a1, a2…a8, b1…b8, c1 and so on to h8. At each turn, only the unit standing on the square which comes earliest in this order may move. However check and mate are normal.

Circe: Captured units (not Ks) reappear on their game-array squares, of the same colour in the case of pieces, on the file of capture in the case of pawns, and on the promotion square of the file of capture in the case of fairy pieces. If the rebirth square is occupied the capture is normal.

Equihopper(EQ): Moves along any line over another unit of either color to a square situated such that the hurdle stands at the mid-point between the Equihopper’s departure and arrival squares. The English Equihopper cannot pass over an obstruction other than the hurdle when playing along Queen-lines. The non-stop/French Equihopper does not have this restriction. Unless otherwise stated, the non-stop Equihopper is meant.

Contra Grasshopper(CG): Moves like a Grasshopper but in reverse: the hurdle must be adjacent to the CG, which may land anywhere on the line beyond. (Grasshopper(G): Moves along Q-lines over another unit of either color to the square immediately beyond that unit. A capture may be made on arrival, but the hurdle is not affected.)