A clamp assembly (465, 565, 601) for securing a rail in place on a rail train, the clamp assembly (465, 565, 601) comprising: a rail support (403, 603) upon which a base of the rail can be supported with a head of the rail extending above the base of the rail; a clamping member for engaging the head of the rail to restrain longitudinal movement of the rail relative to the rail support; a first wedge having a first wedge surface sloping downward relative to said rail support (403, 603) along a first longitudinal direction and a second wedge having a second wedge surface sloping downward relative to said rail support along a second longitudinal direction opposite said first longitudinal direction; the clamping member comprising a first clamping member (467, 604) including a first rail engaging member (472, 571, 629) and a first wedge engaging surface, the first wedge engaging surface advanceable across the first wedge surface toward a lower end thereof to draw the first rail engaging member (472, 571, 629) downward against the head of the rail positioned between the first rail engaging member (472, 571, 629) and the rail support (403, 603) to restrain movement of the rail relative to the rail support in the first longitudinal direction; characterized in that the clamping member comprises a second clamping member (467, 604) including a second rail engaging member (472, 571, 629) and a second wedge engaging surface, the second wedge engaging surface advanceable across the second wedge surface toward a lower end thereof to draw the second rail engaging member downward against the head of the rail positioned between the second rail engaging member (472, 571, 629) and the rail support (403, 603) to restrain movement of the rail relative to the rail support in the second longitudinal direction. a rail support (403, 603) upon which a base of the rail can be supported with a head of the rail extending above the base of the rail; a clamping member for engaging the head of the rail to restrain longitudinal movement of the rail relative to the rail support; a first wedge having a first wedge surface sloping downward relative to said rail support (403, 603) along a first longitudinal direction and a second wedge having a second wedge surface sloping downward relative to said rail support along a second longitudinal direction opposite said first longitudinal direction; the clamping member comprising a first clamping member (467, 604) including a first rail engaging member (472, 571, 629) and a first wedge engaging surface, the first wedge engaging surface advanceable across the first wedge surface toward a lower end thereof to draw the first rail engaging member (472, 571, 629) downward against the head of the rail positioned between the first rail engaging member (472, 571, 629) and the rail support (403, 603) to restrain movement of the rail relative to the rail support in the first longitudinal direction; characterized in that the clamping member comprises a second clamping member (467, 604) including a second rail engaging member (472, 571, 629) and a second wedge engaging surface, the second wedge engaging surface advanceable across the second wedge surface toward a lower end thereof to draw the second rail engaging member downward against the head of the rail positioned between the second rail engaging member (472, 571, 629) and the rail support (403, 603) to restrain movement of the rail relative to the rail support in the second longitudinal direction.