The discovery of the second Kracht group
SOHO's images have been posted on its website since 1999 May. Terry Lovejoy was the first internet user to discover a SOHO comet in 1999 August. Five weeks later, he found a non-Kreutz group comet. It was designated C/1999 R1 (MPEC 1999-R19). Brian Marsden wrote (IAUC 7251):

COMET C/1999 R1 (SOHO)
D. A. Biesecker, SM&A Corporation and Goddard Space Flight Center,
reports observations of what is presumably a comet, not a Kreutz
sungrazer, discovered by T. Lovejoy in SOHO/LASCO C3 data and later
also recognized in earlier C2 data. Astrometry and orbital computations
are given on MPEC 1999-R19. Biesecker also provides the following
LASCO magnitudes, reduced using the Hipparcos Input Catalogue:
Sept. 5.47 UT, 6.6; 5.53, 6.5; 5.57, 6.4; 5.61, 6.3; 5.65, 6.2;
5.70, 6.2; 5.78, 6.4; 5.82, 6.4; 5.86, 6.7; 5.90, 6.9; 5.99, 6.9;
6.07, 7.4; 6.15, 7.4. No tail was detected.

Three years later, Rob Matson found another non-Kreutz group comet first in C2 images and later in C3 images. Only one hour after he had posted his find, I wrote:

Congrats!
It moves very close to the apparent track
of C/1999 R1 with the right speed.
So it's certainly related to C/1999 R1
and there could evolve another new group.

The comet was designated C/2002 R5. Brian Marsden wrote (MPEC 2002-S35, IAUC 7984):

C/2002 R5 appears to be related to C/1999 R1, a point first made by R. Kracht; 

Finally, Kazimieras Cernis found another non-Kreutz group comet in C2 images of 2003 September 08 and later in C3 images. I wrote:

Congrats Kazimieras!
The apparent track (and velocity) in C2 is similar to the
tracks (and velocities) of the low inclination SOHO comets 
C/1999 R1 and C/2002 R5.

Derek Hammer had left  in 2003 August and so there was nobody to measure the positions of the new comet.
I derived a prelininary orbit from my own measurements and sent it to Brian Marsden. The orbit was similar to the
orbits of C/1999 R1 and C/2002 R5.
In 2003 December Karl Battams began measuring and reporting the SOHO comets to CBAT. Karl had a lot of comets to catch up on and
measured Kazimieras comet 2004 April 30. The comet was designated C/2003 R5 (MPEC 2004-J59) May 13. Brian Marsden wrote:

R. Kracht remarked already last September on the similarity of the
motion of what is now called C/2003 R5 to the motions of his proposed pair
C/1999 R1 and C/2002 R5 (see MPEC 2002-S35), fortuitously observed at the
same time of the year.  The above orbit is essentially identical with that of
C/1999 R1 on MPEC 1999-R19.

On 2004 May 17 the new group was announced by Daniel Green (IAUC 8340):

C/2003 R5 belongs to a new group that certainly includes
C/1999 R1 and probably includes C/2002 R5.

Orbital elements of the second Kracht group comets compared with those of the other new groups (2004 July):

The weights are the lengths of the observation times (last obs - first obs).

Sebastian Hönig has sucessfully linked C/1999 R1 = C/2003 R5 (Identification of a new short-period comet near the sun).
He predicts the next return for about 2007 September 11.

Integrating his orbit backwards with Solex 9.1, I have found these approximate perihelion dates:

1995 September 04 (before SOHO and after SMM)

1991 August 28 (before SOHO and after SMM)

1987 August 19 (SMM images available)

Unfortunately the path of this comet is outside the SOHO LASCO C2 field in mid-August.The C2 FOV is about 3.5 x 3.5 degrees.The SMM FOV is about 3.0 x 3.0 degrees (four quadrants around the sun, each measuring 1.5 x 1.5 degrees).

The return of C/1999 R1 = C/2003 R5

Bo Zhou found the returning comet in LASCO C2 images of 2007 September 10 19:31 - 21:30 UTC moving very close to the prediction of Sebastian Hönig. Later, I found it entering the C2 field at 2007 September 10 06:54 with an approximate magnitude of mag 9. It was visible in C3 until about 2007 Sep 11 06:18 UTC. It reached mag 5.5 shortly after perihelion in C3. I could not find it in STEREO SECCHI COR2A images close to peak brightness though they showed stars to mag 10. This is a strong argument for the cometary nature of this object.

Elements from MPEC 2007-S16, Integration to 2011 with Solex.

The orbital elements (peri, node, incl) changed quite a bit between 2003 and 2007. This is due to a moderately close approach (<1.4 AU) to Jupiter in May/June 2006.
The comet was observed to be a bit brighter (mag 5.5 instead of mag 6) than at his previously observed two returns.

It will be interesting to see the evolution of this comet. Will it show fragments? Unfortunately, there is only one instrument at this time to show the comet: SOHO LASCO shows the comet close to its perihelion times. It could be lost, if SOHO LASCO will not be operating 2011 September 06/07.
Perhaps Earth based instruments can image the comet, but it will be quite faint at the larger solar elongations.

The perihelion dates have not much changed with the new orbit from MPEC 2007-S16:
1995 September 03
1991 August 26
1987 August 17
1983 August 08

The return of C/2002 R5 = C/2008 L6 and L7

2008 June 10 I found a comet in LASCO C2 which moved on the track of C/2002 R5. It was accompanied by a small leading fragment. I could link the observations of the new comet with those of C/2002 R5. The orbital period is 5.8 years, similar the orbital periods of the Kracht and Marsden group comets.

2008 July 24 Brian Marsden issued MPEC 2008-O23, in which he wrote:

Comets C/2008 L6 and L7 appear to be members of the "Kracht 2" Group, and
R. Kracht suggests that they represent a return of comet C/2002 R5 (cf. MPEC
2002-S35). The 15-deg shift in the line of nodes actually supports the
likely correctness of this linkage, as it is consistent with the comet's
passage within 1.1 AU of Jupiter in Jan. 2007.

Z. Sekanina derived the time of breakup of C/2002 R5 into its fragments C/2008 L6 and C/2008 L7 as most probably between 2 and 10 weeks before the 2002 perihelion and gave an elliptical solution for C/2008 L7 (IAUC 8983, 2008 September 28).

The previous perihelion of C/2002 R5 = 2008 L6 was 1996 November 25.3. The apparent path crosses the C2 field from about November 25.1 - 25.6, but the comet was not found in these images.

Orbital evolution of P/2007 R5 and C/2008 L6

Light curves of the "Kracht2 group" comets